HSC Board

A simple pendulum performs S.H.M of period 4 seconds. How much time after crossing the mean position, will the displacement of the bob be one third of its amplitude.

As per the given question we can put some data like,

Period T= 4s

displacement is,

$https://latex.codecogs.com/gif.image?\dpi{100} x=\frac{A}{3}$

To find = the time required for displacement to be A/3

Since the particle starts from the mean position the equation for displacement is given as,

x = A sin (ωt)

$https://latex.codecogs.com/svg.image?\frac{A}{3}= A sin(\frac{2\pi t}{T})$

$https://latex.codecogs.com/svg.image?\frac{1}{3}=sin(\frac{2\pi t}{4})$

$https://latex.codecogs.com/svg.image?0.3333=sin(\frac{\pi t}{2})$

$https://latex.codecogs.com/svg.image?\frac{\pi t}{2}= sin^{-1}(0.3333)$

$https://latex.codecogs.com/svg.image?\frac{\pi t}{2}= 19^{0}28^{'}= 19.47^{0} = \frac{19.47\pi }{180} rad$

$https://latex.codecogs.com/svg.image?\frac{t}{2}=\frac{19.47}{180}$

t = 0.2163 s

i.e after 0.2163 s crossing the mean position, the bob will have a displacement of A/3

The mass of the earth is 6 x 10²⁴ kg. The distance between the earth and the Sun is 1.5x 10¹¹ m. If the gravitational force between the two is 3.5 x 10²² N, what is the mass of the Sun?