Question

A 20g particle moves in SHM with a frequency of 3 oscillations per second and amplitude of 5 cm. The total distance does the particle move during one oscillation is
A- 10cm
B- 15cm
C- 20cm
D- 25cm

Answer 1

Hint : As, the particle is oscillating with the frequency of 3 per second and the amplitude is 5 cm, therefore to complete one complete oscillation the particle has to complete one cycle, to complete one cycle the particle has to move from one extreme to the other extreme again it has to come to the mean position. So, in total the particle has to travel four times from mid to extreme position.

Complete Step By Step Answer:
Given, the frequency of the oscillation is 3 per second. It means in one second it oscillates 3 times, so this is the frequency, $f=3hz$
So, $\omega =2\pi f$
$w=2\pi \times 3=6\pi rad/s$
The particle travels from the mean location to one extreme of one oscillation and then back to the mean and then to the other extreme and then to the mean, which means four times the amplitude.
So, the distance moved by the particle in one oscillation will be $4\times 5=20$ . Well, that accounts for 20 cm.

Note :
This is a question of wave oscillation, Simple periodic motion is that the action under which the restore force on the moving target is directly proportional to the displacement magnitude of the object. Amplitude is the maximum displacement of any object from the mean position.
Also, here the mass is misleading and has no use in the calculations, it is just there to confuse the students.