Maximum speed in SHM

2 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 \(\mathrm { m } \mathrm { s } ^ { - 1 }\), 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 \(2.50 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), correct to 3 significant figures.

1 A particle \(P\) is moving with simple harmonic motion in a straight line. The period is 6.1 s and the amplitude is 3 m . Calculate, in either order,

1. the maximum speed of \(P\),
2. the distance of \(P\) from the centre of motion when \(P\) has speed \(2.5 \mathrm {~ms} ^ { - 1 }\).

1 A particle is moving with simple harmonic motion in a straight line. The period is 0.2 s and the amplitude of the motion is 0.3 m . Find the maximum speed and the maximum acceleration of the particle.

2 The movement of a particle is described by the simple harmonic equation $$\ddot { x } = - 25 x$$ where \(x\) metres is the displacement of the particle at time \(t\) seconds, and \(\ddot { x } \mathrm {~m} \mathrm {~s} ^ { - 2 }\) is the acceleration of the particle. The maximum displacement of the particle is 9 metres. Find the maximum speed of the particle.
Circle your answer.
[0pt] [1 mark]
\(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
\(45 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
\(75 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
\(135 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)