Question 1 : <div>State whether true or false.<br/></div>All periodic motion need not be oscillatory but all oscillatory motions<br/>are periodic.

Question 2 : <div>State whether true or false.<br/></div>Piston of the engine in a motor car exhibits <span>Oscillatory motion.</span>

Question 6 : The equation of motion of a particle is $x = a \cos (a t)^{2}$. The motion is

Question 7 : Swinging of table fan is an example of which type of motion?

Question 9 : The displacement of a particle varies with time, according to the equation $y = a \sin \omega t + b \cos \omega t$

Question 12 : Motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower point is

Question 13 : If a particle is oscillating on the same horizontal plane on the ground.

Question 15 : The motion described by the needle of sewing machine is oscillatory motion. True or false

Question 16 : Time period of oscillation of a spring is $12$s on earth. What shall be the time period if it is taken to moon?

Question 19 : When a vibrating tuning fork is placed on a table, a large sound is heard. This is due to<span><br></span>

Question 20 : The vertical extension in a light spring by a weight of $1\ kg$ suspended from the wire is $9.8\ cm$. The period of oscillation:

Question 22 : The period of a pendulum is 0.20 seconds. What is the frequency of the pendulum?

Question 23 : &#34;A bird flapping its wings circles around a clock tower&#34;. Which part of the motion is periodic and oscillatory ?

Question 24 : A spring has a certain mass suspended from it and its period for vertical oscillation is $T$. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillation is now

Question 25 : The equation of motion of a particle is $x = a cos(\alpha t)^2$. The motion is

Question 26 : An object with a mass M is suspended from an elastic spring with a spring constant k. The object oscillates with period T. If the mass of oscillations is quadrupled, how it will change the period of oscillations?<br>

Question 27 : <div>State whether true or false.<br/></div>Rotation of moon around the earth is a periodic motion.

Question 28 : The equation x =a sin 2t + b cos 2t will represent an SHM

Question 29 : In the equations below, A, B, $\omega$ and $\phi$ are constants; $y$ and $t$ are variables; $t$ represents time. Only one of the following equations does not represent SHM. Which one is that?

Question 30 : <p>For a particle showing motion number under the force$F = - 5{\left( {x - 2} \right)^2}$ , the motion is</p>

Question 32 : If a body moves back and forth repeatedly about a mean position, it is said to possess

Question 35 : "The projection of the path of a particle in a circle along its diameter is an oscillatory motion" Is this statement correct

Question 36 : Assertion: The time period of a simple pendulum is independent of its length. Reason: The length of a pendulum is the distance between point of suspension and centre of the bob

Question 37 : Calculate the period and frequency for the second hand, minute hand, and hour hand of a clock.

Question 38 : Which of the following is true of all systems displaying simple harmonic motion?

Question 39 : During the oscillations of a simple pendulum, the string takes the same path as that of the bob, then:

Question 41 : The time period of a particle executing SHM is $\displaystyle \frac{2\pi}{\omega}$ and its velocity at a distance $b$ from mean position is $\sqrt{3}b\omega$. Its amplitude is<br/>

Question 42 : &#34;The motion of a particle with a restoring force gives oscillatory motion&#34;. Which of the following force can be a restoring force for the oscillatory motion.

Question 43 : A particle is moving in a circular path with continuously increasing speed. Its motion is<br>

Question 44 : Assertion: We can call circular motion also as simple harmonic motion. Reason: Angular velocity in uniform circular motion and angular frequency in simple harmonic motion have the same meanings.

Question 45 : By suspending a mass of 0.50 kg, a spring is stretched by 8.20 m. If a mass of 0.25 kg is suspended, then its period of oscillation will be :<div>(Take g = 10 $ms^{-2}$)<br/></div>

Question 46 : Which of the following characteristics must remain constant for undamped oscillations of the particle?<br>

Question 47 : Which of the following quantities is non-zero at the mean position for a particle executing SHM?<br>

Question 48 : A pan with a set of weights is attached to a light spring. The period of vertical oscillation is $0.5 s$. When some additional weights are put in pan, then the period of oscillations increases by $0.1 s$. The extension caused by the additional weight is

Question 49 : A particle of mass $2\ kg$ is moving on a straight line under the action of force $F=(8-2x)N$. The particle is released at rest from $x=6\ m$. For the subsequent motion select the correct options:<br>

Question 50 : <span>The frequency of a particle executing SHM is 10 Hz. The particle is suspended from a vertical spring. At the highest point of its oscillation, the spring is unstretched. Maximum speed of the particle is $(g = 10 m/s2)$</span>

Question 52 : Two pendulums differ in lengths by $22\ cm$. They oscillate at the same place so that one of them makes $30$ oscillations and the other makes $36$ oscillations during the same time. The lengths (in cm) of the pendulums are

Question 54 : A light spiral spring supports a 200 g weight at its lower end. It oscillates up and down with a period of 1 sec. How much weight (gram) must be removed from the lower end to reduce the period to 0.5 sec.?

Question 55 : A simple harmonic motion has an amplitude $A$ and time period $T$. The time required by it to travel $x = A$ to $x = \dfrac {A}{2}$ is:

Question 56 : Assertion : Every periodic motion is not simple harmonic motion.<br>Reason : The motion governed by the force law<br>$F = -kx$ is simple harmonic.

Question 57 : A particle is describing simple harmonic motion. If its velocities are $v_{1}$ and $v_{2}$ when the displacements from the mean position are $y_{1}$ and $y_{2}$ respectively, then its time period is

Question 58 : A particle is moving on a circle with uniform speed. Its motion is<br>

Question 59 : <div>State whether true or false.<br/></div><div><br/></div>Motion of the needle of a sewing machine is rotatory motion.

Question 60 : A mass is suspended from a spring having spring constant '$K$' is displaced vertically and released, it oscillates with period '$T$'. The weight of the mass suspended is ($g =$ gravitational acceleration)

Question 61 : The displacement of a particle along the x-axis is given by $x=a\sin^2\omega t$. The motion of the particle corresponds to.

Question 62 : <div>State whether true or false.<br/></div>The needle of a moving sewing machine executes o<span>scillatory motion.</span>

Question 63 : A particle of mass $m$ moving along the $x-$ axis as a potential energy $U(x)=a+bx^2$ where $a$ and $b$ are positive constants. It will execute simple harmonic motion with a frequency determined by the value of :

Question 64 : A particle executes simple harmonic motion between $x=-A$ and $x=+A$. The time taken for it to go from $0$ to $A/2$ is $T_1$ and to go from $A/2$ to A is $T_2$. Then.

Question 65 : For a particle performing SHM, equation of motion is given as $\displaystyle \frac{d^{2}x}{dt^{2}}+4x=0$. Find the time period

Question 66 : A particle is executing simple harmonic motion with an amplitude $A$ and time period $T$. The displacement of the particles after $2 T$ period from its initial position is

Question 67 : The amplitude and the periodic time of a SHM are $5cm$ and $6s$ respectively. At a distance of $2.5cm$ away from the mean position, the phase will be

Question 68 : A particle vibrating simple harmonically has an acceleration of $16{cms}^{-2}$ when it is at a distance of $4cm$ from the mean position. Its time period is

Question 69 : If at any instant of time the displacement of a harmonic oscillator is $0.02\ \text{m}$ and its acceleration is $2\ \text{ms}^{-2}$, its angular frequency at that instant will be<br>

Question 70 : The bye-bye gesture, we do using hands is an example of

Question 71 : If a spring has time $T$, and is cut into $n$ parts , then the time period of each part will be

Question 72 : A simple harmonic motion along the $x$-axis has the following properties: amplitude = $0.5\ m$, the time to go from one extreme position to other is, $2\ s$ and $x = 0.3\ m$ at $t = 0.5\ s$. The general equation of the simple harmonic motion is<br>

Question 73 : Equation of SHM is x = 10 sin 10 $\pi$t. Then the time period is, x is in cm and t is in sec

Question 74 : If a SHM is given by y = ($sin \omega t + cos \omega t$)m, which of the following statement is true?

Question 75 : A particle moves in a circular path with a uniform speed. Its motion is

Question 76 : What is the angular frequency of oscillation of the block after the acceleration ceases?

Question 77 : The pendulum of a bob undergoes SHM with an amplitude A is given by the equation $y= A sin \omega t$. The corresponding angular SHM equation can be written as

Question 78 : The displacement of a particle is represented by the equation<br/>$y = 3 \cos \left [ \dfrac{\pi }{4} - 2\omega t \right ]$ the motion of the particle is <br/>

Question 79 : The equation of displacement of a particle executing SHM is $x=0.40 \cos(2000 t+18)$. The frequency of the particle is<br/>

Question 80 : The force which tries to bring the body back to its mean position is called<span><br></span>

Question 81 : Simple harmonic oscillation of a given system can be specified completely by stating its: <br/>

Question 83 : <span>A simple pendulum has time period $T _ { 1 }.$ The point of suspension is now moved upward according to equation $y = K t ^ { 2 }$ where $K = 2.5 \mathrm { m } / \mathrm { s } ^ { 2 }.$ If new time period is $T _ { 2 }$ then ratio will be</span>

Question 85 : Assertion : Simple harmonic motion is the projection of uniform circular motion on the diameter of the circle in which the later motion occurs.<br>Reason : Simple harmonic motion is a uniform motion.

Question 86 : Name the type of motion in which a girl is skipping a rope at a particular spot

Question 87 : A particle of mass $m$ moves in a straight line. If $v$ is the velocity at a distance $x$ from a fixed point on the line and $v^{2}=a-bx^{2}$, where $a$ and $b$ are constant then:

Question 88 : Assertion: In case of oscillatory motion the average speed for any time interval is always greater than or equal to its average velocity. Reason: Distance travelled by a particle cannot be less than its displacement.

Question 89 : A particle executing S.H.M. completes a distance (taking friction as negligible) in one complete one time period.

Question 90 : The time taken by a particle performing S.H.M. to pass from point A to B where its velocities are same is $2$ seconds. After another $2$ seconds, it returns to B. Determine the time period of oscillation is (in seconds).

Question 91 : A simple harmonic oscillator of angular frequency 2 rad $s^{-1}$ is acted upon by an external force $F= sin tN.$ If the oscillator is at rest in its equilibrium position at t=0, its position at later times is proportional to

Question 93 : A particle is performing SHM of amplitude &#34;A&#34; and time period &#34;T&#34;. Find the time taken by the particle to go from 0 to A /$\sqrt{2}$.

Question 94 : A thin fixed ring of radius 1m has a positive charge $1 \times 10^{-5}$ C uniformly distributed over it. A particle of mass 0.9 g and having a negative charge of $1 \times 10^-6$ C is placed on the axis at a distance of 1 cm from the centre of the ring. Calculate the time period of oscillations.

Question 95 : The angular frequency of a spring block system is $\omega _{0}$ This system is suspended from the ceiling of anelevator moving downwards with a constant speed v$_{0}$. The block is at rest relative to the elevator. Lift issuddenly stopped. Assuming the downwards as a positive direction, choose the wrong statement:

Question 96 : A particle of mass $10 g$ lies in a potential field $v = 50 x^2 + 100$. The value of frequency of oscillations in Hz is:<br/>

Question 97 : A particle moves along the $x$-axis according to the equation $x = 10 sin3 ( t )$. The amplitudes and frequencies of component SHMs are<br/>

Question 98 : Assertion: In $SHM$, acceleration is always directed towards the mean position. Reason: In $SHM$, the body has to stop momentary at the extreme position and move back to mean position.

Question 99 : A particle is executing SHM along a straight line. Its velocities at distances $x_1 $ and $x_2$ from the mean position are $V_1$ and $V_2$ respectively. Its time period is:

Question 100 : Assertion: Path of a particle in SHM is always a straight line. Reason: All straight line motions are not simple harmonic.