Question 1 : <span>The displacement x of a particle in motion is given in terms of time by x (x - 4) = 1&#160;- 5 $\cos \omega t$</span>

Question 2 : For a body in $S.H.M$ the velocity is given by the relation $v=\sqrt{144-16x^2}m/sec$. The maximum acceleration is&nbsp;&nbsp;

Question 3 : <span>A particle in SHM has maximum velocity $V _ { \max }$&nbsp;&nbsp;at mean position and amplitude r. Its velocity when the displacement&nbsp; is 1/3 amplitude is</span>

Question 4 : A simple pendulum performs simple harmonic motion about $<span><span>X=0$</span></span><span>&nbsp;with an amplitude&nbsp;$4$ cm</span><span>&nbsp;and time period $2$ sec</span><span>. The speed of the pendulum at $\frac {A}{2}$</span><span>&nbsp;will be (in cm/s)</span><br>

Question 5 : In SHM the net force towards mean position is related to its displacement (x) from mean position by the relation

Question 6 : A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any&nbsp;displacement $x$ is proportional to:

Question 7 : When the bob of a pendulum is at the mean position (minimum displacement) of its motion, its total energy is

Question 9 : The potential energy of a weight less spring compressed by a distance $a$, is proportional to

Question 10 : Two spring of force constant 300 N/m (spring A )&#160; and&#160; 400 N/m (spring B) are joined together in series. The combination is compressed by 8.75 cm. The ratio of energy stored in A and B is&#160;$\frac{E_{A}}{E_{B}}$

Question 11 : The equation of a simple harmonic wave is given by&nbsp; $y=3sin\frac{\pi }{2}(50t-x)$ where x and y are in meters and t is in seconds. The ratio of maximum particle velocity to the wave velocity is:<br>

Question 12 : Two bodies M and N of equal mass are suspended from two separate massless spring of force constant $k_1$ and $k_2$ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of vibration of M to that of N is?

Question 13 : A particle execute SHM with time period $T$ and amplitude $A$. The maximum possible average velocity in time $\dfrac {T}{4}$:

Question 14 : The length of a simple pendulum is 1 m. The bob is given a velocity $ 7 m s^{-1} $ in a horizontal direction from near position. During upward motion of bob, if the string breaks when it is horizontal, then the maximum vertical height of an ascent of bob from rest position is<br/><br/>

Question 15 : A particle moving along the $x-$axis execute simple harmonic motion, then the force acting on it is given by

Question 16 : &#160;A particle executes S.H.M with a period of 6 seconds. If the maximum speed is 3.14 cm/sec, then what is its amplitude?<br/>

Question 17 : 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:<br/>

Question 18 : A sine wave has an amplitude $A$ and a wavelength $\lambda$ Let $v$ be the wave velocity, and $V$ be maximum velocity of a particle in the medium.

Question 19 : Three particles $\alpha$-particle, proton and deuteron are accelerated by the same potential difference. What is the ratio of kinetic energy :

Question 20 : Two particles $P$ and $Q$ start from origin and execute simple harmonic motion along $X-$ axis with same amplitude but with periods $3\&#160; s$ and $6\&#160; s$ respectively. The ratio of the velocities of<b><i>&#160;</i></b>$P$ and $Q$ when they meet is&#160;

Question 21 : An instantaneous displacement of a simple harmonic oscillator is $x=A\cos \left(\omega t+\dfrac{\pi}{4} \right)$. Its speed will be maximum at

Question 22 : The amplitude of an oscillating simple pendulum is 10 cm and its time period is 4s. Its speed after is when it passes through its equilibrium position is :

Question 23 : For a mass on a spring, which is maximized when the displacement of the mass from its equilibrium position is zero?&nbsp;

Question 24 : At what position along a straight line will the velocity be zero for a particle executing SHM

Question 25 : The force constants of two springs are $K_1$ and $K_2$. Both are stretched till their elastic energies are equal. If the stretching forces are $F_1$ and $F_2$, then $F_1 : F_2$ is&nbsp;

Question 26 : The pendulum bob has a speed of 3m/s at its lowest position. The pendulum is 0.5 m long. The speed of the bob, when the bob makes an angle of $60^\circ$ to the vertical will be ($g = 10 m/s^2$)

Question 27 : A cork floating on the pond water executes a simple harmonic motion, moving up and down over a range of $4\ cm$. The time period of the motion is $1\ s$. At $t=0$, the cork is at its lowest position of oscillation, the position and velocity of the cork at $t=10.5\ s$, would be

Question 28 : The time period of an oscillating body executing SHM is 0.05 sec and its amplitude is 40 cm.The maximum velocity of particle is

Question 29 : The bob (mass $m$) of a simple pendulum of length $L$ is held horizontal and then released. It collides elastically with a block of equal mass lying on a frictionless table. The kinetic energy of the block will be

Question 30 : Consider a semi- circular shell of mass m and&#160;radius r which rolls without slipping as shown&#160;in Fig. use the fact that maximum kinetic energy&#160;at mean position is equal to maximum&#160;potential energy at extreme position to find&#160;out the frequency of oscillation:<br/>

Question 31 : A particle is executing simple harmonic motion of amplitude $A$. At a distance $x$ from the centre, a particle moving towards the extreme position receives a blow in the direction of motion which instantaneously doubles the velocity. Its new amplitude will be<br/>

Question 32 : The equation of displacement of a particle executing simple harmonic motion is x = (5m)&nbsp;$\displaystyle \sin \left [ (\pi s^{-1})t+\frac{\pi }{3} \right ]$. Write down the amplitude, time period and maximum speed. Also find the velocity at t = 1s.

Question 33 : A block whose mass is $1$kg is fastened to a spring. The spring has a spring constant of $100Nm^{-1}$. The block is pulled to a distance $x = 10$cm from its equilibrium position at $x= 0$ on a frictionless surface from rest at $t = 0$. The kinetic energy and potential energy of the block when it is $5$cm away from the mean position is

Question 34 : The energy of a particle executing simple harmonic motion is given by E = $ Ax^2 + Bv^2 $ where $x$ is the&nbsp;displacement from mean position $x =0$ and $v$ is the velocity of the particle at $x$ then choose the correct&nbsp;statement(s).

Question 35 : Two springs $P$ and $Q$ of force constants $k_p$ and $k_Q\left(\displaystyle k_Q=\frac{k_p}{2}\right)$ are stretched by applying forces of equal magnitude. If the energy stored in $Q$ is $E$, then the energy stored in $P$ is?

Question 36 : A spring is loaded with two blocks $m_1$ and $m_2$ where $m_1$ is rigidly fixed with the spring and $m_2$ is just kept on the block $m_1$. The maximum energy of oscillation is possible for the system having the block $m_2$ in contact with $m_1$ is&#160;

Question 37 : The angular velocity and the amplitude of simple pendulum is $\omega$ and $a$ respectively. At a displacement $X$ from mean position, if the kinetic energy is $T$ and potential energy is $V$. Then ratio $T$ to $V$

Question 38 : A simple pendulum of length 1 m has a bob of mass 200 g. It is displaced ${ 60 }^{ \circ&nbsp; }$ and then released. Find the kinetic energy of the bob when<br>It passes through the mean position

Question 39 : A simple pendulum of length&nbsp; $\ell$&nbsp; carries a bob of mass&nbsp; $m.$&nbsp; When the bob is at its lowest position, it is&nbsp;given&nbsp;the minimum horizontal speed necessary for it to move in a vertical&nbsp;circle about the point of&nbsp;suspension. When the string is horizontal, the net force on the bob is

Question 40 : A $1.8$ g mass suspended by a spring with a spring constant of $3$ N/m is forced to oscillate in viscous medium (b=$2$ g/s) by a driving force of F=${10^{ - 3}}$ sin$40$t (in SI units). the amplitude of the driven oscillations will be

Question 42 : A hydrogen atom has mass $1.68\times 10^{-27}$kg. When attached to a certain massive molecule it oscillates with a frequency $10^{14}$ Hz and with an amplitude $10^{-9}$ cm. Find the force acting on the hydrogen atom.<br>

Question 43 : A particle oscillates simple harmonically with a period of 16 s. Two second after crossing the equilibrium position its velocity becomes 1 m/s. The amplitude is<br/>

Question 44 : A block rides on a piston that is moving vertically with simple harmonic motion. The maximum speed of the piston is $2m/s$. At what amplitude of motion will the block and piston separate? $(g=10m/s^{2})$<br/>

Question 45 : <p><span>A steamer moves with velocity 3 km/h in and against the direction of river water whose velocity is 2 km/h. Calculate the total time for the total journey if the boat travels 2 km in the direction of a stream and then back to its place:</span></p>

Question 46 : <div><span>A particle executing simple harmonic motion has an angular frequency of 6.28 $\displaystyle s^{-1}$ and amplitude of 10 cm, find&#160;</span><span>the speed at t = 1/6 s assuming that the motion starts from rest at t = 0.</span></div>

Question 47 : A particle of mass $m$ moves according to the equation $F=-amr$ where $a$ is a positive constant$, r$ is radius vector. $r=r_0\hat{i}$ and $v=v_0\hat{j}$ at $t=0$. Describe the trajectory.<br>

Question 48 : A mass $m$, which is attached to a spring with constant $k$, oscillates on a horizontal table, with amplitude $A$. At an instant when the spring is stretched by ${\sqrt{3}A}/{2}$, a second mass $m$ is dropped vertically onto the original mass and immediately sticks to it. What is the amplitude of the resulting motion?

Question 49 : A particle performs simple harmonic motion with amplitude A. Its speed is tripled at the instant that it is at a distance $\displaystyle\frac{2A}{3}$ from equilibrium position. The new amplitude of the motion is.

Question 50 : A practice is executing SHM. its time period is equal to the smallest time interval in which the particle acquires a particular velocity,$\bar { v } $, the magnitude of $\bar { v } $ may be: