A simple pendulum with spring constant 500n/m oscillates between two points x1 = 10cm and x2 = 15 cm. What is total mechanical energy at 10cm?
Correct answer: C. 1562.5J
- A. 1000J
- B. 6250J
- C. 1562.5J
- D. None of these
Explanation
The total mechanical energy of a simple harmonic oscillator is constant and is given by: E = 1/2 kA^2where:E is the total mechanical energyk is the spring constantA is the amplitude of oscillationThe amplitude is the maximum displacement from the equilibrium position. In this case, the amplitude is:apache - x1) / 2 = (15 cm - 10 cm) / 2 = 2.5 cm = 0.025 mTherefore, the total mechanical energy at 10 cm is: E = 1/2 * 500 N/m * (0.025 m)^2 = 1562.5 J
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About Simple Harmonic Motion
Simple harmonic motion is oscillation in which acceleration is directly proportional to displacement and directed toward the equilibrium position. Work includes displacement, velocity, acceleration, phase, period, frequency, amplitude and energy, with applications to springs and simple pendulums. The restoring force and the conditions for SHM distinguish it from general periodic motion.
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