Question

The oscillators that can be described in terms of sine or cosine functions are called

• A. simple harmonic
• B. natural
• C. sympathetic
• D. free

Answer 1

The correct option is A simple harmonic

In simple harmonic motion, displacement of a particle is directly proportional to restoring force.
$F\propto -x\Rightarrow F=-kx\Rightarrow m\frac{d^{2}x}{d{t}^2}=-kx$.
The solution of the above equation can be given by
$x=c_1\cos \left(\omega t\right)+c_2\sin \left(\omega t\right)=A\sin (\omega t-\varphi )$, where
$A=\sqrt{c_1^2+c_2^2}$, $\omega =\sqrt{\frac{k}{m}}$ and $\varphi ={\tan }^{-1}\left(\frac{c_2}{c_1}\right)$
$c_1$ and $c_2$ are constants and values can be determined from the initial boundary conditions.
So simple harmonic motions can be described as sin or cosine functions.
Ans: $A$