If a simple pendulum oscillates with small amplitude and its length is doubled, what happens to the frequency of its motion? (a) It doubles. (b) It becomes times as large. (c) It becomes half as large. (d) It becomes times as large. (e) It remains the same.
Option (d) is the correct answer, i.e it becomes times as larger.
A simple pendulum of length L can be modeled to move in simple harmonic motion for small angular displacements from the vertical. Its period is
Period of oscillation
Length of pendulum
The period of a simple pendulum is
, and its frequency is
Thus, if the length is doubled so , the new frequency is
Hence option (d) is the correct answer for this question.
You attach a block to the bottom end of a spring hanging vertically. You slowly let the block move down and find that it hangs at rest with the spring stretched by 15.0 cm. Next, you lift the block back up to the initial position and release it from rest with the spring unscratched. What maximum distance does it move down? (a) 7.5 cm (b) 15.0 cm (c) 30.0 cm (d) 60.0 cm (e) The distance cannot be determined without knowing the mass and spring constant.
A object attached to a spring moves without friction (b=0) and is driven by an external force given by the expression , where F is in Newton’s and t is in seconds. The force constant of the spring is . Find
(a) The resonance angular frequency of the system,
(b) The angular frequency of the driven system, and
(c) The amplitude of the motion.
Review: A large block P attached to a light spring executes horizontal, simple harmonic motion as it slides across a frictionless surface with a frequency . Block B rests on it as shown in Figure and the coefficient of static friction between the two is . What maximum amplitude of oscillation can the system have if block B is not to slip?
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