Simple Harmonic Motion [Mechanics] 2012

Simple Harmonic Motion (SHM)

Question1

A particle oscillates in simple harmonic motion with centre O. When its distance from O is 3 m its speed is 16 m s−1, and when its distance from O is 4 m its speed is 12 m s−1. Find the period and amplitude of the motion.

Question 2

A particle P, of mass 0.2 kg, moves in simple harmonic motion along a straight line under the action of a resultant force of magnitude F N. The distance between the end-points of the motion is 0.6 m, and the period of the motion is 0.5 s. Find the greatest value of F during the motion.

Question 3

The tip of a sewing-machine needle oscillates vertically in simple harmonic motion through a distance of 2.10 cm. It takes 2.25 s to perform 100 complete oscillations. Find, in m s −1, the maximum speed of the tip of the needle.

Show that the speed of the tip when it is at a distance of 0.5 cm from a position of instantaneous rest is 2.50 m s−1, correct to 3 significant figures.

Question 4

A particle P moves on a straight line AOA’ in simple harmonic motion with period T. The centre of the motion is O and P is instantaneously at rest at A and A’. The mid-points of OA and OA’are B and B’respectively.

(i) Find, in terms of T, the time for P to move directly from B to B’.

(ii) Find the ratio of the speed of P at B to its speed at O.

Question 5

A particle rests on a horizontal platform which oscillates vertically in simple harmonic motion with period 2.5 seconds. During the motion the particle does not leave the platform. Show that the greatest possible value of the amplitude of the motion is approximately 1.58 m. [5] In the case when the amplitude is exactly 1.58 m the lowest position of the particle is at the point A. Find the time for the particle to move directly to B, where AB = 2 m.

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