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Simple Harmonic Motion (SHM) and Hooke's Law

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1. A 300-g mass at the end of a spring oscillates with an amplitude of 7.0 cm and a frequency of 1.80 Hz. (a) Find its maximum speed and maximum acceleration. (b) What is its speed when it is 3.0 cm from its equilibrium position?
A) 8.96 m/s, 8.9 m/s2 (b) 0.45 m/s
B) 79.2 m/s, 895 m/s2 (b) 0.512 m/s
C) 0.79 m/s, 8.9 m/s2 (b) 0.72 m/s
D) 0.0062 m/s, 0.00055m/s2 (b) 0.0056 m/s

2. With a 50-g mass at its end, a spring undergoes SHM with a frequency of 0.70 Hz. How much work is done in stretching the spring 15 cm from its unstretched length? How much energy is then stored in the spring?
A) 0.011 J, 0.011 J
B) 1.1 J, 1.1 J
C) 110 J, 110 J
D) 0.073 J, 0.073 J

3. A certain Hookean spring is stretched 20 cm when a given mass is hung from it. What is the frequency of vibration of the mass if pulled down a little and released?
A) 1.1 Hz
B) 44 Hz
C) 0.11 Hz
D) 7.80 Hz

4. A 300-g mass at the end of a spring executes SHM with a period of 2.4 s. Find the period of oscillation of a 133-g mass attached to the same spring.
A) 1.6 s
B) 0.033 s
C) 24.7 s
D) 0.41 s

5. Find the frequency of vibration on Mars for a simple pendulum that is 50 cm long. Objects weigh 0.40 as much on Mars as on the Earth.
A) 0.057 Hz
B) 17.8 Hz
C) 2.22 Hz
D) 0.45 Hz

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Solution Summary

This solution is comprised of a detailed step-by-step calculation and explanation of the given problems related to Simple Harmonic Motion (SHM) and Hooke's Law. This solution provides students with a clear perspective of the various aspects of Simple Harmonic Motion like Frequency of Vibration, Angular Frequency, Amplitude of Vibration, Maximum Speed, Maximum Accleration, Equilibrium Position, Time Period, Potential Energy, Work Done etc.

Solution provided by:
  • MSc, Osmania University
  • MSc, Indian Institute of Technology - Roorkee (I.I.T.-ROORKEE)
  • BSc, Banaras Hindu University
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