Question

If x, v and a represent the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T then which of the following does not change ?

• A. $\frac{aT}{v}$
• B. $aT+2\pi v$
• C. $\frac{aT}{x}$
• D. $a^2{T}^2+2{\pi }^2{v}^2$

Answer 1

The correct option is C $\frac{aT}{x}$

Given:

Displacement= x

Velocity=V

Acceleration=a

For SHM partical,

$a={\omega }^{2}x$ ...........(1)

$\omega =\frac{2\pi }{T}$

On putiong the value of $\omega$ in equation (1)

$a={\left(\frac{2\pi }{T}\right)}^{2}x$

$4{\pi }^2=\frac{a{T}^2}{x}$

$\frac{4\pi }{T}=\frac{aT}{x}$........(2)

From equation (2) $LHS$ is constant hence $RHS$ will be constant.

Option C