Question

A mass is suspended from a vertical spring and the system is allowed to come to rest. When the mass is now pulled down a distance of 76mm and released, the time taken for 25 oscillations is 23s.
Find the displacement of the mass from its rest position 0.6s after being released. State the direction of this displacement.

The answer is -43.1mm upward, but I am not sure how to work out the direction?

Answer 1

The oscillation period is 23/25 = 0.920 seconds. 0.6 seconds is 0.65217 periods after the maximum displacement, so the phase angle is x = 4.0977 radiansafter maximum downward displacement.
Displacement @ t=0.6 s (with + being down)
= 76 mm*(cos x)
= 76 mm*(-0.57668)
= -43.8 mm (- is upward)
I believe my -43.8 mm answer is more accurate than the -43.1 that you quote.