A simple pendulum has a period of 2.5 s. (i) what is its period if its length is made four times larger? (a) 1.25 s (b) 1.77 s (c) 2.5 s (d) 3.54 s (e) 5 s (ii) What is its period if the length is held constant at its initial value and the mass of the suspended bob is made four times larger? Choose from the same possibilities.
(a)The period if its length is made four times larger is, Hence option (e) is the correct answer for this question.
(b) The period if the length is held constant at its initial value and the mass of the suspended bob is made four times larger is, Hence option (c) is the correct answer for this question.
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
From step (1), we have
and , where i and f stands for initial and final respectively.
The period becomes larger by a factor of 2, to become 5 s.
Hence option (e) is the correct answer for this question.
Changing the mass has no effect on the period of a simple pendulum.
Hence option (c) is the correct answer for this question.
A block with mass m = 0.1 kg oscillates with amplitude A = 0.1 m at the end of a spring with force constant k = 10 N/m on a frictionless, horizontal surface. Rank the periods of the following situations from greatest to smallest. If any periods are equal, show their equality in your ranking. (a) The system is as described above. (b) The system is as described in situation (a) except the amplitude is 0.2 m. (c) The situation is as described in situation (a) except the mass is 0.2 kg. (d) The situation is as described in situation (a) except the spring has force constant 20 N/m. (e) a small resistive force makes the motion under damped.
A light, cubical container of volume is initially filled with a liquid of mass density as shown in Figure P15.89a. The cube is initially supported by a light string to form a simple pendulum of length, measured from the center of mass of the filled container, where . The liquid is allowed to flow from the bottom of the container at a constant rate . At any time, the level of the liquid in the container is and the length of the pendulum is(measured relative to the instantaneous center of mass) as shown in Figure P15.89b. (a) Find the period of the pendulum as a function of time. (b) What is the period of the pendulum after the liquid completely runs out of the container?
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