Question

A horizontal platform with an object placed on it is executing SHM in the vertical direction. The amplitude of oscillation is 2.5 cm. what must be the least period of these oscillations so that the object is not detached from the platform? Take g = 10 $m{s}^{-2}$

• A. $0.1\pi sec$
• B. $0.5\pi sec$
• C. $\pi$
• D. $2\pi sec$

Answer 1

The correct option is A $0.1\pi sec$

The object will not detach from the platform, if the angular frequency $\omega$ is such that, during the down ward motion, the maximum acceleration equals athe acceleration due to gravity, i.e.,
${\omega }_{max}^{2}A=g$
or ${\omega }_{max}=\sqrt{\frac{g}{A}}$
or $T_{min}=\frac{2\pi }{{\omega }_{max}}=2\pi \sqrt{\frac{A}{g}}$
Now A=2.5 cm=2.5 $\times {10}^{-2}m$ and g=$10m{s}^{-2}$
Substituting these values we get, T = 0.1 $\pi$ sec