The variations of potential energy (U) with position x for three … - Vidyadip

MCQ

The variations of potential energy $(U)$ with position $x$ for three simple harmonic oscillators $A, B$ and $C$ are shown in figure. The oscillators have same mass. The time period of oscillation is greatest for

A
$A$
B
$B$
✓
$C$
D
Same for all

✓

Answer

Correct option: C.

$C$

c
(c)

$U=\frac{1}{2} k x^2$

$x^2=\frac{2 U}{k}$

or $x \propto \frac{1}{k}$ (Since $U$ is constant)

Also $T=2 \pi \sqrt{\frac{m}{k}}$

or $T \propto \frac{1}{\sqrt{k}}$

Therefore $x \propto T$

Hence the oscillation with maximum $x$ will have the maximum time period.

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