1.To arrive at the relationship between displacement, velocity and acceleration for a system in SHM 2.To be able calculate the magnitude & direction of the acceleration at any time for an object in SHM Book Reference : Pages 36-37

Displacement Amplitude T/2 T The sine wave above shows the displacement of an object such as a simple pendulum which is moving with SHM Now draw the velocity & acceleration on the same axis

Displacement Amplitude T/2 T Velocity

+ - 0 Amplitude T/2 T Acceleration

r Our pendulum is in uniform circular motion.  the acceleration is given by:- a = v 2 / r & v = 2  rf  a = (2  rf) 2 / r  a = (2  f) 2 r For SHM..... Acceleration = - (2  f) 2 x displacement

A mass on a spring oscillates in SHM with amplitude 25mm & a period of 2s. If it passes the equilibrium in the upwards direction at time t=0 what is the displacement of the object: ¼ cycle later, ½ cycle later, ¾ cycle later & 1 cycle later? Calculate : The frequency [0.5Hz] Acceleration when displacement is +25mm, 0 & - 25mm [-25x10 -3  2 ms -2, 0, 25x10 -3  2 ms -2 ]

A simple pendulum oscillates in SHM with an amplitude of 32mm. It takes 20s to complete 10 complete oscillations. Calculate: a.The frequency [0.5Hz] b.The initial acceleration [ ms -2 ] If the pendulum is released at time t=0, state the displacement and calculate the acceleration when t = 1.0s and t = 1.5s [32mm (other side), ms -2 & 0,0]