1.1. To arrive at the relationship between To arrive at the relationship between displacement, velocity and acceleration for a displacement, velocity and acceleration for a system in SHMsystem in SHM

2.2. To be able calculate the magnitude & To be able calculate the magnitude & direction of the acceleration at any time for direction of the acceleration at any time for an object in SHMan object in SHM

Book Reference : Pages 36-37Book Reference : Pages 36-37

Dis

plac

emen

t +

-

0

Amplitude

Amplitude

T/2

T

The sine wave above shows the displacement The sine wave above shows the displacement of an object such as a simple pendulum which of an object such as a simple pendulum which is moving with SHMis moving with SHM

Now draw the velocity & acceleration on the Now draw the velocity & acceleration on the same axis same axis

Dis

plac

emen

t +

-

0

Amplitude

Amplitude

T/2

T

+

-

0

Velo

city

Velo

city

+

-

0

Amplitude

Amplitude

T/2

T

+

-

0

Acc

eler

atio

n

r

Our pendulum is in uniform circular motion. the acceleration is given by:-

a = v2 / r & v = 2rf

a = (2rf)2 / ra = (2f)2 r

For SHM.....

Acceleration = - (2f)2 x displacement

A mass on a spring oscillates in SHM with amplitude A mass on a spring oscillates in SHM with amplitude 25mm & a period of 2s. If it passes the equilibrium 25mm & a period of 2s. If it passes the equilibrium in the upwards direction at time t=0 what is the in the upwards direction at time t=0 what is the displacement of the object:displacement of the object:

¼ cycle later, ½ cycle later, ¾ cycle later & 1 cycle ¼ cycle later, ½ cycle later, ¾ cycle later & 1 cycle later?later?

Calculate :Calculate :

The frequency The frequency [0.5Hz][0.5Hz]

Acceleration when displacement is +25mm, 0 & -Acceleration when displacement is +25mm, 0 & -25mm 25mm [-25x10[-25x10-3-322 ms ms-2-2, 0, 25x10, 0, 25x10-3-322 ms ms-2-2] ]

A simple pendulum oscillates in SHM with an A simple pendulum oscillates in SHM with an amplitude of 32mm. It takes 20s to complete 10 amplitude of 32mm. It takes 20s to complete 10 complete oscillations. Calculate:complete oscillations. Calculate:

a.a. The frequency The frequency [0.5Hz][0.5Hz]

b.b. The initial acceleration The initial acceleration [-0.316 ms[-0.316 ms-2-2]]

If the pendulum is released at time t=0, state the If the pendulum is released at time t=0, state the displacement and calculate the acceleration when t displacement and calculate the acceleration when t = 1.0s and t = 1.5s = 1.0s and t = 1.5s [32mm (other side), 0.316 ms[32mm (other side), 0.316 ms-2-2 & 0,0] & 0,0]