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Q1. The light balloon filled with helium of density 0.18 kg/m3 is tied to the light string of length L = 3 m. The string is tied to ground, forming an ‘inverted’ simple pendulum. When the balloon is displaced slightly from equilibrium, show that the motion is simple harmonic and find out the period of motion. Take the density of air to be 1.29 kg/m3.

Q2. Expectant parents are thrilled to hear their unborn baby’s heart beat, disclosed by an ultrasound motion detector. Assume the fetus’s ventricular wall moves in the simple harmonic motion with amplitude 1.80 mm and frequency 115 per minute.

a) Find out the maximum linear speed of the heart wall. Assume that the motion detector in contact with the mother’s abdomen produces sound at exactly 2 MHz, which travels via the tissue at 1.50 km/s.

b) Find out the maximum frequency at which the reflected sound is received through the motion detector. (By electronically listening for echoes, the detector can generate beeps of sound.)

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