Question

A particle is performing simple harmonic motion in a straight line with time period 12 second the minimum time taken by the particle to cover a distance equal to Amblitude will be​

Answer 1

Given that,

Time period of the particle in SHM is, T = 12 s

To find,

The time taken by the particle to cover a distance equal to amplitude.

Solution,

The general equation of SHM is given by :

$y=A\sin\omega t$

y = displacement

A is amplitude

t is time taken

Here, y = A

So,

$A=A\sin\omega t\\\\\sin\omega t=1$

Since, sin(90) = 1

$\sin\omega t=\sin 90\\\\\omega t=\dfrac{\pi}{2}\\\\\dfrac{2\pi }{T}\times t=\dfrac{\pi}{2}$

Since, $\omega=\dfrac{2\pi }{T}$

So,

$t=\dfrac{T}{4}\\\\t=\dfrac{12}{4}\\\\t=3\ s$

So, the minimum time taken by the particle to cover a distance equal to amplitude is 3 seconds.