Question

A particle executes SHM of time period 10 sec. The displacement of particle at any instant is x = 10 sinωt(cm) Find 

1. Velocity of body 2 s after it passes through mean position. 

2. Acceleration of body 2 s after it passes mean position.

Answer 1

Given x = 10 sin ωt T = 10 sec

A = 10 cm ω = \(\frac{2π}{10}\) rad/s

Let at t = 0 body be at the mean position.

Now at t = 2

1. V = Aω cos ωt

= 10ω cos(ω²)cm/s

⇒ V = 1.94 cm/s

2. Acceleration

a = – Aω² sinωt

⇒ a = – 3.75 cm/s².