Question

A simple pendulum, composed of a bob of mass $m$ connected to the end of a massless rod, executes simple harmonic motion as it swings through small angles of oscillation.The maximum angular displacement with the vertical is denoted by ${\theta }_{max}$. Frictional effects and variation of acceleration due to gravity are negligible.
Find out the correct statement?

• A. At $\theta =0$, the tangential acceleration is $0$
• B. At $\theta ={\theta }_{max}$, the tangential acceleration is $0$
• C. At $\theta =0$, the speed is $0$
• D. At $\theta =0$, the restoring force is maximized
• E. At $\theta ={\theta }_{max}$, the speed is maximized

Answer 1

The correct option is A At $\theta =0$, the tangential acceleration is $0$

We know the tangential acceleration in SHM is given by

$a=-{\omega }^{2}A\sin \theta$

where $A=amplitude$

therefore at $\theta =0$

$a=-{\omega }^{2}A\sin 0^0$

or $a=0$ because $\sin 0^0=0$