Question 88: Oscillations

Question

The point A moves with a uniform speed along the circumference of a circle of radius 0.36 m and covers 30$$^\circ$$ in 0.1 s. The perpendicular projection 'P' from 'A' on the diameter MN represents the simple harmonic motion of 'P'. The restoration force per unit mass when P touches M will be :

Accepted Answer

The point a covers 30$$^\circ$$ in 0.1 sec.
Means $${\pi  \over 6}\buildrel {} \over
 \longrightarrow 0.1$$ sec.
$$1\buildrel {} \over
 \longrightarrow {{0.1} \over {{\pi  \over 6}}}$$
$$2\pi  \buildrel {} \over
 \longrightarrow {{0.1 	imes 6} \over \pi } 	imes 2\pi $$
$$T = 1.2$$ sec.
We know that $$\omega  = {{2\pi } \over T}$$
$$\omega  = {{2\pi } \over {1.2}}$$
Restoration force $$(F) = m{\omega ^2}A$$
Then Restoration force per unit mass $$\left( {{F \over m}} ight) = {\omega ^2}A$$
$$\left( {{F \over m}} ight) = {\left( {{{2\pi } \over {1.2}}} ight)^2} 	imes 0.36$$
$$ \cong 9.87$$ N

Answer

9.87 N

Answer

0.49 N

Answer

50 N

Answer

100 N

Oscillations

The point A moves with a uniform speed along the circumference of a circle of radius 0.36 m and covers 30$^\circ$ in 0.1 s. The perpendicular projection 'P' from 'A' on the diameter MN represents the simple harmonic motion of 'P'. The restoration force per unit mass when P touches M will be :

Choose the correct answer: