A block of mass $15 k g$ executes $S H M$ under the restoring force of a spring. The amplitude and the maximum force of the motion are $0.1 m$ and $6 N$ respectively. Find the time period of the motion?

314 s

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31.4 s

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3.14 s

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2.24 s

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Solution

The correct option is B $3.14 s$
The maximum force acting on block in SHM= $k x_{m a x} = k A$
$= m ω^{2} A = F_{m a x}$
$⟹ ω = \sqrt{\frac{F_{m a x}}{m A}}$
$= \sqrt{\frac{6}{15 \times 0.1}} = 2$
Hence the time period of the SHM= $T = \frac{2 π}{ω}$
$= π \approx 3.14 s$

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A block of mass 15kg executes SHM under the restoring force of a spring. The amplitude and the maximum force of the motion are 0.1m and 6N respectively. Find the time period of the motion?

The correct option is B 3.14sThe maximum force acting on block in SHM=kxmax=kA=mω2A=Fmax⟹ω=√FmaxmA=√615×0.1=2Hence the time period of the SHM=T=2πω=π≈3.14s

A block of mass $15 k g$ executes $S H M$ under the restoring force of a spring. The amplitude and the maximum force of the motion are $0.1 m$ and $6 N$ respectively. Find the time period of the motion?

The correct option is B $3.14 s$
The maximum force acting on block in SHM= $k x_{m a x} = k A$
$= m ω^{2} A = F_{m a x}$
$⟹ ω = \sqrt{\frac{F_{m a x}}{m A}}$
$= \sqrt{\frac{6}{15 \times 0.1}} = 2$
Hence the time period of the SHM= $T = \frac{2 π}{ω}$
$= π \approx 3.14 s$