JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Elasticity & SHM

In the figure given below, a block of mass

M = 490

g placed on a frictionless table is connected with two springs having same spring constant (

K = 2

N m

^{- 1}

). If the block is horizontally displaced through 'X' m then the number of complete oscillations it will make in

14 π

seconds will be _____

Answer: 20

Solution

With the block held between the two walls, a displacement stretches one spring and compresses the other, and both push it back, so they act in parallel with effective constant

K_{e f f} = K + K = 4

N m

^{- 1}

. The period is

T = 2 π \frac{M}{K _{e f f}} = 2 π \frac{0.49}{4} = 2 π \times \frac{0.7}{2} = \frac{7 π}{10}

s. In

14 π

s the number of complete oscillations is

\frac{14 π}{7 π /10} = 20

JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Integer answer

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