MCQ
Mark the wrong statement
- AAll S.H.M.’s have fixed time period
- ✓All motion having same time period are S.H.M.
- CIn S.H.M. total energy is proportional to square of amplitude
- DPhase constant of S.H.M. depends upon initial conditions
✓
Answer
Correct option: B.
All motion having same time period are S.H.M.
b
For SHM, the force of the particle is given by,
For SHM, the force of the particle is given by,
$F =- kx$
$\Rightarrow ma =- kx$
$\Rightarrow a =\frac{- k }{ m } x$
We also have,
$a=-\omega^2 x$
From this, we can say $\omega^2=\frac{k}{ m }$
or, $\omega^2=\sqrt{\frac{ k }{ m }}$, which is a constant.
Now, time period is given by, $T =\frac{2 \pi}{\omega}$ which will also be a constant. Hence,
option $A$ is right.
All motion which have same period may not be SHM. $A$ good example is that
of when a particle is moving in a circle. This case has same time period but is
not an example of SHM. Hence, the wrong answer is $B$.
The total energy of SHM is given by, $KE =\frac{1}{2} kA ^2$. So, we can see that the total
energy is directly proportional to the square of amplitude. Hence, option $C$ is
also correct.
The phase constant is given by $y=A \sin \omega t+\phi$ where $\phi$ is the phase constant.
Clearly we can see that the phase constant depends directly upon the initial
condition of the particle. Hence, option $D$ is also correct.
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