Question

Which physical quantity oscillates with the same frequency as that of SHM for a harmonic oscillator?

• A. acceleration
• B. $E_{total}$
• C. KE
• D. PE

Answer 1

The correct option is A acceleration

The general equation of a SHM is given by $x=A\sin (wt\pm \varphi )$ where $w$ is the angular frequency, $A$ be the amplitude, $\varphi$ be the phase angle.

Acceleration $a=-A{w}^2\sin (wt\pm \varphi )$

$E_{total}=\frac{1}{2}m{w}^2{A}^2$

$KE=\frac{1}{2}m{w}^2(A^2-x^2)=\frac{1}{2}m{w}^2{A}^2[1-\frac{1}{2}\times 2{\sin }^2(wt\pm \varphi \left)\right]$

$=\frac{1}{2}m{w}^2{A}^2[1-\frac{1}{2}(1-cos(2wt\pm 2\varphi )\left)\right]$

$PE=\frac{1}{2}m{w}^2{x}^2=\frac{1}{4}m{w}^2{A}^2\times 2{\sin }^2(wt\pm \varphi )=\frac{1}{2}m{w}^2[1-cos(2wt\pm 2\varphi \left)\right]$

Thus, the acceleration will oscillate with same frequecy $w$ as that of SHM , total energy will not oscillate and KE and PE will oscillate with frequency $2w$.