Question

1.

a) A machine part is undergoing SHM with a frequency of 4.95 Hz and amplitude 1.85 cm. How long does it take the part to go from x=0 to x=? 1.85 cm?

bi) An object is undergoing SHM with period 0.930 s and amplitude 0.320 m. At t = 0, the object is at x = 0.320 mand is instantaneously at rest. Calculate the time it takes the object to go from x = 0.320 m, to x = 0.160 m.

bii) Calculate the time it takes the object to go from x = 0.160 m, to x = 0.

Answer 1

a] It is given that the frequency is 4.95 Hz

so, the time period is: T = 1/f = 0.202 s

for the part to go from x=0 to x=1.85cm (amplitude), One-Quarter of a wave is complete.

Therefore, the time to reach from x=0 to x=1.85cm is:

t = T/4 = 0.0505s

bi] The period of the motion is 0.93s

at t = 0s, x = 0.32m (amplitude)

and to reach x=0, it takes one-quarter of a wave period (T/4)

so, to reach x = 0.16m (which is half of the amplitude), the time taken will be:

t = (T/4)/2 = T/8 = 0.11625s

bii] The time it will take to go from x=0.16m to x =0 will be the same as the time it took to reach from x=0.32m to x=0.16m which is t = 0.11625s.