Question

A particle is executing SHM. Find the positions of the particle where its speed is 8 cm/s, If maximum
magnitudes of its velocity and acceleration are 10 cm/s and 50 cm/s2
respectively.

Answer 1

Answer:

Using x = A sin w t    then

v(max) = w A

a(max) = w^2 A   omitting the sign

w = 50 / 10 = 5    dividing equations    

v(max) = 10 = 5 * A     so A = 2

v = A w cos w t

When v = 8      cos wt = 8 / (2 * 5) = .8

so wt = 36.9 deg

x = 2 * sin 36.9 = 1.2 cm

So the particle has a speed of 8 cm/s at +- 1.2 cm