Simple Harmonic Motion Q and A
Summarize:
In a study of simple harmonic motion, various phenomena were analyzed. Firstly, when a mass-spring system has its mass released from a position double its original distance, the oscillation frequency remains consistent, denoted as �. Secondly, upon increasing the amplitude of a mass vibrating on a spring, there’s a notable increase in its maximum speed and kinetic energy, though its period remains unaffected. In a specific scenario involving a 0.500 kg glider on a spring with a force constant of 450 N/m oscillating with a 0.040 m amplitude, the calculations revealed a maximum speed of 1.2 m/s, a speed of 1.11 m/s at a displacement of �=−0.015�, and a maximum acceleration of 36 m/s^2. Additionally, its total mechanical energy was found to be 0.36 J, and its motion was described by the equation �=−1.2���(30�). Furthermore, a pendulum exhibiting a 1.60 s period on Earth would have a 2.60 s period on Mars, considering Mars’ gravitational acceleration of 3.71 m/s^2. Lastly, a 2.50 kg rock swinging from a 1.45 m long rope, initially released at 11° and later rising to only 4.5° after 10.5 swings, was found to have lost 0.544 J of energy. This energy loss was primarily attributed to its conversion to heat, minor conversion to sound due to air resistance, and potential friction at the pendulum’s pivot point.
Excerpt:
Simple Harmonic Motion Q and A
Simple Harmonic Motion
Q.1 When a mass attached to a spring is released from rest 3.0 cm from its
equilibrium position, it oscillates with frequency 𝑓. If this mass were
instead released from rest 6.0 cm from its equilibrium position, it would
oscillate with a frequency equal to
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Simple Harmonic Motion
Q.2 Suppose you increase the amplitude of oscillation of a mass vibrating on
a spring. Which of the following statements about this mass are correct?
(There may be more than one correct choice)
Answer:
a) Its maximum speed increases.
b) Its period of oscillation increases.
c) Its maximum acceleration increases.
d) Its maximum kinetic energy increases.
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