JEE Main · 2023 · 06 Apr 2023 · Shift 1 · Elasticity & SHM

A mass m is attached to two springs as shown in figure. The spring constants of two springs are

K_{1}

and

K_{2}

. For the frictionless surface, the time period of oscillation of mass

m

Answer: (C)

Solution

When the mass is displaced by distance

x

to the right, both springs exert restoring forces toward equilibrium.

Net force:

F = - (k_{1} x + k_{2} x) = - (k_{1} + k_{2}) x

Acceleration:

a = \frac{F}{m} = - \frac{k _{1} + k _{2}}{m} x = - ω^{2} x

Angular frequency:

ω = \frac{k _{1} + k _{2}}{m}

Time period:

T = \frac{2 π}{ω} = 2 π \frac{m}{k _{1} + k _{2}}

JEE Main · 2023 · 06 Apr 2023 · Shift 1 · Single correct option