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From eqns. (7) and (8), tan o, %3D, and, A =, or, =tan!, 14.5. SIMPLE HARMONIC MOTION, Define and explain simple harmonic motion., Simple harmonic motion : A particle executes S.H.M. if it moves to and fro about a fixed point such th, acceleration at any instant is directly proportional to its displacement at that instant but the direction of, acceleration is opposite to the direction of the displacement., F = 0, Consider a spring whose one end is tied to a hook A and a body llll, of mass M is attached to the other end as shown in figure 7 (a)., The body of mass M is assumed to be lying on a frictionless, surface as shown in figure 7 (a). The spring is unstretched and this, position of the body of mass M is called equilibrium position, IX=0, Fext, مقوو, M, which is denoted by x 0. Let us apply an external force Fer to, stretch the spring as shown in Fig. 7 (b). Let the displacement of, the mass M from the equilibrium position be x. As soon as the, eem, x =0, external force is applied, another force F called restoring force, comes into play which is equal and opposite to the applied external, Figure 7, force i.e. F=-Feu. It is this restoring force, which brings the, body or the system to its original position, when the external force is removed., According to Hooke's Law, the displacement of the body is directly proportional to the applied external force., That is,, Fext x, But, Fext, =-F, Fa-X, F--k X, or, or, where K is constant of proportionality and known as force constant or spring constant., Eqn.(1) is known as force law., If a is the acceleration produced in the block of mass M, then according to Newton's second law of motion, F=Ma, From eqns. (1) and (2), we get Ma -k s, or a, ->, MX, k, is constant, therefore, a o, M, Since, Thus, acceleration of the block is directly proportional to its displacement and the direction of acceleration is opposite, direction of the displacement. Hence, motion of the block is simple harmonic motion (S.H.M.)., A particle or a body executing simple harmonic motion (S.H.M.) is called simple harmonic oscillator., 14.5.1 SpRing CONSTANT OR FORCE CONSTANT, Define Spring or Force constant. State units of Jorce constant and write its dimensional formula, Force constant or spring constant : The jorce constant is defined as the restoring force per unit displaceme.

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437, L.Y OSCILLATIONS AND WAVES-Oscillations, We know,, F=-kx, .k =, Units of spring constant :, 1. In CGS system, unit of spring constant (k) is dyne/cm (or dyne cm-)., 2. In SI, unit of spring constant (k) is newton/metre (Nm-)., de, MLT2, =[ML°T*], [니, Dimensional Formula of spring constant =, Dimensional formula of force, !!, Dimensional formula of distance, ENOTE Dimensional formula of spring constant is same as that of surface tension., Numerical Example 3. A spring stretches by 15cm when a body of mass 2-5 kg is suspended from its free end., Calculate the spring constant of the spring., Solurion. Here, x = 15 cm = 0-15 m, m =2-5 kg, .. F = mg =2-5 x 9-8%324-5 N, 24-5N, Now, spring constant,, k =-=, = 163-33 Nm-1, 0-15m