First slide

Simple hormonic motion

Question

A particle of mass l0 gm is placed in a potential field given by V = (50 $x^{2}$ + 100) J/kg. The frequency of oscillation in cycle/sec is

Moderate

A

$\frac{10}{π}$
B

$\frac{5}{π}$
C

$\frac{100}{π}$
D

$\frac{50}{π}$

Solution

Potential energy U = mV
$\Rightarrow U = (50 x^{2} + 100) 10^{- 2}$
F = $- \frac{dU}{dx} = - (100 x) 10^{- 2}$
$\Rightarrow {mω}^{2} x = - (100 \times 10^{- 2}) x$
$10 \times 10^{- 3} ω^{2} x = 100 \times 10^{- 2} x$
$\Rightarrow ω^{2} = 100 ∴ ω = 10$
$\Rightarrow f = \frac{ω}{2 π} = \frac{10}{2 π} = \frac{5}{π}$

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