Question

An object performing a SHM has a maximum acceleration of 8pai m s-2 and maximum velocity of 1.6 m s-1. What is its amplitude and period?​

Answer 1

The amplitude and period are 10.1 cm and 0.4 s.

Step-by-step explanation:

Given that,

The maximum acceleration of an object in SHM,
`a=8\pi\ m/s^2`

The maximum velocity of the object,
`v=1.6\ m/s`

The formula for the maximum velocity and acceleration in SHM is given by :

`v=A\omega\ ....(1)\\\\a=A\omega^2\ ....(2)`

Dividing equation (1) and (2) :

`(v)/(a)=(A\omega)/(A\omega^2)\\\\(v)/(a)=(1)/(\omega)\\\\\omega=(a)/(v)\\\\(2\pi)/(T)=(a)/(v)\\\\T=(2\pi v)/(a)\\\\T=(2\pi * 1.6)/(8* \pi)\\\\T=0.4\ s`

Also,

`\omega=(8\pi)/(1.6)\\\\=15.7\ rad/s`

Pu in equation (1) to find A,

`A=(v)/(\omega)\\\\=(1.6)/(15.7)\\\\=0.101\ m\\\\=10.1\ cm`

So, the amplitude and period is 10.1 cm and 0.4 s.