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 spring constant k, the period of oscillation of the body (assuming the springs as massless) is

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 spring constant k, the period of oscillation of the body (assuming the springs as massless) is (A) 2 π(M / 2 k)1 / 2 (B) 2 π(2 M / k)1 / 2 (C) 2 π(M g sin θ / 2 k) (D) 2 π(2 M g / k)1 / 2

Tardigrade Admin · Accepted Answer

It is a system of two springs in parallel. The restoring force on the body is due to springs and not due to gravity pull. Therefore slope is irrelevant.
Here the effective spring constant

= k + k = 2 k

∴

Time period

= 2 π \frac{M}{2 k}

Q. 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 spring constant $k$ , the period of oscillation of the body (assuming the springs as massless) is

$2 π (M /2 k)^{1/2}$

$2 π (2 M / k)^{1/2}$

$2 π (M g sin θ /2 k)$

$2 π (2 M g / k)^{1/2}$

It is a system of two springs in parallel. The restoring force on the body is due to springs and not due to gravity pull. Therefore slope is irrelevant.
Here the effective spring constant $= k + k = 2 k$
$∴$ Time period $= 2 π \frac{M}{2 k}$

Q. 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 spring constant k, the period of oscillation of the body (assuming the springs as massless) is

2π(M/2k)1/2

2π(2M/k)1/2

2π(Mgsinθ/2k)

2π(2Mg/k)1/2