Question

A particle executes simple harmonic motion between x = – a and x = +
a. the time taken for it to go from o to a/2 is t1 and to go from a/2 to a is t2. then how t1 and t2 will be related? please explain the answer in brief

Answer 1

Given:

A particle executes simple harmonic motion between x = – a and x = +

a.

The time taken for it to go from o to a/2 is t1 and to go from a/2 to a is t2.

To Find:

How t1 and t2 will be related.

Solution:

For a simple harmonic motion ,

• displacement , x = asinωt

Therefore, given at t1 , x = a/2 ==>

• sinωt1 = 1/2 = >
• ωt1 = π/6
• t1 = π/6ω - (1)

Also t2 is the time take for particle to travel from a/2 to a.

• let the particle be at a at time = t .
• x = a , at time = t
• ωt = π/2

• Therefore t2 = t - t1
• t2 = π/2ω - π/6ω = π/3ω - (2)
• t2 = 2t1

Therefore t2 will be related to t1 as t2 = 2t1.