At the end points =±A x The velocity of the particle = 0, v Acceleration = 2A directed towards the mean position, a kinetic energy =0 T potential energy =1/2 m2A2=E V (ii) At the mid-point (x = 0), REFERENCE CIRCLE Suppose that the point is moving anticlockwise with uniform angular velocity a Q circular path with as the centre (Fig. 1.2). This circle is called the reference circle for simple O harmonic motion. any diameter of the circle. is chosen to be along the B′OB x-axis. From a perpendicular is dropped on the diameter When moves with uniform Q, QP B′B. Q angular velocity along the circular path, the point executes simple harmonic motion along the P diameter The amplitude of the back and forth motion of the point about the centre is BB′. P O OB = the radius of the circle = Suppose is at at time = 0 and it takes a time for going from A. Q B t t to and by this time the point moves form to If B Q P B P. When completes one revolution along the circular path, the point executes one complete Q P oscillation. The time period of oscillation = If we choose the circle in the plane, the T xy 2π/. position of at any time is given by Q t THE SIMPLE PENDULUM The bob of the simple pendulum undergoes nearly SHM if its angle of swing is not large. The time period of oscillation of a simple pendulum of length is given by l
At the end points x =±A The velocity of the particle v = 0, Acceleration a = 2A directed towards the mean position, kinetic energy T =0 potential energy V =1/2 m2A2=E (ii) At the mid-point (x = 0), REFERENCE CIRCLE Suppose that the point Q is moving anticlockwise with uniform angular velocity a circular path with O as the centre (Fig. 1.2). This circle is called the reference circle for simple harmonic motion. any diameter of the circle. B′OB is chosen to be along the x-axis. From Q, a perpendicular QP is dropped on the diameter B′B. When Q moves with uniform angular velocity along the circular path, the point P executes simple harmonic motion along the diameter BB′. The amplitude of the back and forth motion of the point P about the centre O is OB = the radius of the circle = A. Suppose Q is at B at time t = 0 and it takes a time t for going from B to Q and by this time the point P moves form B to P. If When Q completes one revolution along the circular path, the point P executes one complete oscillation. The time period of oscillation T = 2π/. If we choose the circle in the xy plane, the position of Q at any time t is given by THE SIMPLE PENDULUM The bob of the simple pendulum undergoes nearly SHM if its angle of swing is not large. The time period of oscillation of a simple pendulum of length l is given by