Question 179: Oscillations

Question

A block of a mass 2 kg is attached with two identical springs of spring constant 20 N/m each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is $$\frac{\pi}{\sqrt x}$$ in SI unit. The value of $$x$$ is ____________.

Accepted Answer

Both the springs are in parallel so net spring constant is $K_{	ext {net }}=K_{1}+K_{2}=40 \mathrm{~N} / \mathrm{m}$
So $T=2 \pi \sqrt{\frac{m}{K_{n e t}}}$
$$
\begin{aligned}
& =2 \pi \sqrt{\frac{2}{40}} \\
& =\frac{\pi}{\sqrt{5}}
\end{aligned}
$$
$	herefore x=5$

Oscillations

Integer / Numeric Answer Type