JEE Main · 2023 · 24 Jan 2023 · Shift 1 · Elasticity & SHM

A block of 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{π}{x}

in SI unit. The value of

x

is ____ .

Answer: 5

Solution

With the block sitting between two springs anchored to opposite walls, a displacement

x

stretches one spring and compresses the other, and both push the block back, so the restoring force is

2 k x

and the effective constant is

2 k

. The angular frequency is

ω = \frac{2 k}{m} = \frac{2 ( 20 )}{2} = 20 rad/s

, and the period is

T = \frac{2 π}{20} = \frac{π}{5}

. Comparing with

\frac{π}{x}

, the value of

x

5

JEE Main · 2023 · 24 Jan 2023 · Shift 1 · Integer answer

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JEE Main · 2023 · 24 Jan 2023 · Shift 1 · Elasticity & SHM

Solution

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