section A 1. A spring of force constant, k = 5 N m^-1 , is placed horizontally o
ID: 1870304 • Letter: S
Question
section A
1. A spring of force constant, k = 5 N m^-1 , is placed horizontally on a smooth table. One end of the spring is fixed and a mass, X = 0.2 kg, is attached to the free end. X is displaced a distance of 4 mm and released. Show that the motion of X is simple Harmonic and calculate (a) the period (b) the maximum acceleration (c) the maximum Kinetic Energy (d) the maximum potential Energy of the spring
2. A mass of 0.1 kg oscillates in simple harmonic motion with an amplitude of 0.2m and a period of 0.1 s. Calculate its maximum Kinetic Energy and sketch a graph showing how the energy varies with (i) the displacement (ii) the time. Label key points on the axes.
3. A sound of frequency 200 Hz is emitted from a signal generator with a peak voltage output of 1.5 V.
A microphone attached to a Cathode Ray Oscilloscope picks up the sound.
The time base on the cathode ray oscilloscope is set to 2 ms cm^-1, the y-scale setting is 0.5 V cm^-1
Sketch the waveform seen on the screen, labelling key measurements.
Explanation / Answer
1. k = 5 N / m
m = 0.2 kg
A = 4 mm = 0.004 m
(A) T = 2 pi sqrt(m / k ) = 1.26 sec
(B) a_max = A w^2 and w = 2 pi / T
= (0.004) (2 pi / 1.26)^2
= 0.10 m/s^2
(C) MAx KE = total energy = k A^2 / 2
= 5 x 0.004^2 / 2
= 40 x 10^-6 J
(D) Max PE = total energy = 40 x 10^-6 J
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