Question

On a smooth inclined plane, a body of mass M is attached between two springs. The other ends of the springs are fixed to firm supports. If each spring has force constant K, the period of oscillation of the body (assuming the springs as massless) is

• A. $2\pi {\left(\frac{m}{2K}\right)}^{\frac{1}{2}}$
• B. $2\pi {\left(\frac{2M}{K}\right)}^{\frac{1}{2}}$
• C. $2\pi \frac{Mgsin\theta }{2K}$
• D. $2\pi {\left(\frac{2Mg}{K}\right)}^{\frac{1}{2}}$

Answer 1

The correct option is A

$2\pi {\left(\frac{m}{2K}\right)}^{\frac{1}{2}}$

In this harmonic oscillator, the two springs are in parallel. Since these spings are identical therefore net spring constant of the system would be $K_{eq}=K_1+K_2=2K$

Time period, $T=2\pi \sqrt{\frac{m}{k_{eq}}}$ = $T=2\pi \sqrt{\frac{m}{2K}}$