First slide

Simple harmonic motion

Question

Figure shows the variation of force acting on a particle of mass 400 g executing simple harmonic motion. The frequency of oscillation of the particle is

Moderate

A

$4 s^{- 1}$
B

$(\frac{5}{2 π}) s^{- 1}$
C

$(\frac{1}{8} π) s^{- 1}$
D

$(\frac{1}{2} π) s^{- 1}$

Solution

The slope of the length
$\begin{array}{l} = \frac{F}{x} = - \frac{0.5}{5} = - 0.1 {Ncm}^{- 1} = - 10 {Nm}^{- 1} \\ But F = - m ω^{2} x or, \frac{F}{x} = - m ω^{2} \\ So, - m ω^{2} = - 10 or, m ω^{2} = 10^{\circ} \\ ∴ ω^{2} = \frac{10}{4 \times 10^{- 1}} \Rightarrow ω = \frac{10}{2} = 5 \\ ∴ f = \frac{ω}{2 π} = \frac{5}{2 π} / s \end{array}$

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