Question

A spring block system is put into $\text{SHM}$ in two experiments. In the first experiment, the block is pulled from the equilibrium position through a distance $d_1$ and then released. In the second experiment, it is pulled from the equilibrium position through a greater distance $d_2$ and then released. For the given scenario choose the incorrect statement.

• A. Time period is same for both $\text{SHM}$
• B. Frequency is same for both $\text{SHM}$
• C. Maximum kinetic energy is same for both $\text{SHM}$
• D. Angular frequency is same for both $\text{SHM}$

Answer 1

The correct option is C Maximum kinetic energy is same for both $\text{SHM}$

The time period for a spring-block system performing simple harmonic motion is,
$T=2\pi \sqrt{\frac{m}{k}}$
$\Rightarrow f=\frac{1}{2\pi }\sqrt{\frac{k}{m}}$
Angular frequency is given by,
$\omega =\sqrt{\frac{k}{m}}$
Above parameters $T,f,\omega$ are independent of amplitude but Max. Kinetic energy depends on the amplitude of oscillation.
${\text{K.E}}_{\text{max}}=\frac{1}{2}m{\omega }^2{A}^2$
In the second case, the amplitude of oscillation of block will be higher $(d_2>d_1)$, hence maximum kinetic energy will be greater in this case.