Question

Two particles are executing SHM, one with angular frequency $\omega$ and the other with ${}^{\prime }2{\omega }^{\prime }$. Which of the following acceleration $\left(a\right)$ vs position $\left(x\right)$ graphs correctly represent SHM's of two particles.

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

We know that, if a particle executes SHM, it follows
$a=-{\omega }^{2}x$
For particle $1:a_1=-{\omega }^{2}x$ ... (1)
For particle $2:a_2=-4{\omega }^{2}x$ ... (2)
From (1) and (2) we can say that $a_2=4a_1$
$\therefore a_2$ has more slope than $a_1$
Hence, option (c) is correct