A simple pendulum comprised of a bob of mass m = 172 g and a lightweight string of length 76.0 cm is released from rest from an initial angle of 28.0° from the vertical. (a) Using the approach of simple harmonic motion, what is the maximum speed of the pendulum bob? m/s (b) Using the approach of simple harmonic motion, what is the maximum angular acceleration of the bob? rad/s2 (c) How does the speed found in part (a) compare with that found by using a conservation of energy approach? (Assume that the values are nearly the same if within 10% of each other.) The speed is very different from that from part (a). The speed is nearly the same as that from part (a).
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
A simple pendulum comprised of a bob of mass
and a lightweight string of length 76.0 cm is released from rest from an initial angle of 28.0° from the vertical.
m/s
(b) Using the approach of simple harmonic motion, what is the maximum
rad/s2
(c) How does the speed found in part (a) compare with that found by using a conservation of energy approach? (Assume that the values are nearly the same if within 10% of each other.)
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