Question

body of mass 200 g executing simple
harmonic motion has a velocity of 3 cms^-1
when its displacement is 4 cm and a velocity
of 4 cms^-1when the displacement is 3 cm.
Calculate
(i) amplitude of oscillation, and
(ii) period of oscillation.

Answer 1

i) Velocity of the particle:

$$v^2=\omega^2(A^2-x^2)$$

So

$$4^2=\omega^2(A^2-3^2)$$

$$3^2=\omega^2(A^2-4^2)$$

$$\frac{(A^2-3^2)}{(A^2-4^2)}=\frac{16}{9}$$

$$A=5\ cm$$

ii)

$$4^2=\omega^2(5^2-3^2)$$

$$\omega=1\frac{rad}{s}$$

$$T=\frac{2\pi}{\omega}=\frac{2\pi}{1}=6.28\ s$$