Answered: In a simple pendulum experiment, what…

In a simple pendulum experiment, what kind of graph do you get when you graph the length of the string vs. the period of oscillation?

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter12: Oscillatory Motion

Section: Chapter Questions

Problem 5CQ

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Review. A simple pendulum is 5.00 m long. What is the period of small oscillations for this pendulum if it is located in an elevator (a) accelerating upward at 5.00 m/s2? (b) Accelerating downward at 5.00 m/s2? (c) What is the period of this pendulum if it is placed in a truck that is accelerating horizontally at 5.00 m/s2?
Determine the period of oscillation of a simple pendulum of length L suspended from the ceiling of a car that rolls down an inclined plane of angle (Fig. P16.73). Dissipative forces between the car and the plane are negligible.
A simple pendulum has a length of 52.0 cm and makes 82.0 complete oscillations in 2.00 min. Find (a) the period of the pendulum and (b) the value of g at the location of the pendulum.
A small object is attached to the end of a string to form a simple pendulum. The period of its harmonic motion is measured for small angular displacements and three lengths. For lengths of 1.000 m, 0.750 m, and 0.500 m, total time intervals for 50 oscillations of 99.8 s, 86.6 s, and 71.1s are measured with a stopwatch. (a) Determine the period of motion for each length. (b) Determine the mean value of g obtained from these three independent measurements and compare it with the accepted value. (c) Plot T2 versus L and obtain a value for g from the slope of your best-fit straight-line graph. (d) Compare the value found in part (c) with that obtained in part (b).
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 2 times as large. (c) It becomes half as large. (d) It becomes 1/2 times as large. (e) It remains the same.
A 2.00-kg block lies at rest on a frictionless table. A spring, with a spring constant of 100 N/m is attached to the wall and to the block. A second block of 0.50 kg is placed on top of the first block. The 2.00-kg block is gently pulled to a position x=+A and released from rest. There is a coefficient of friction of 0.45 between the two blocks. (a) What is the period of the oscillations? (b) What is the largest amplitude of motion that will allow the blocks to oscillate without the 0.50-kg block sliding off?
A grandfather clock depends on the period of a pendulum to keep correct time. (i) Suppose a grandfather clock is calibrated correctly and then a mischievous child slides the bob of the pendulum downward on the oscillating rod. Does the grandfather clock run (a) slow, (b) fast, or (c) correctly? (ii) Suppose the grandfather clock is calibrated correctly at sea level and is then taken to the top of a very tall mountain. Does the grandfather clock run (a) slow, (b) fast, or (c) correctly?
It is important for astronauts in space to monitor their body weight. In Earth orbit, a simple scale only reads an apparent weight of zero, so another method is needed. NASA developed the body mass measuring device (BMMD) for Skylab astronauts. The BMMD is a spring-mounted chair that oscillates in simple harmonic motion (Fig. P16.23). From the period of the motion, the mass of the astronaut can be calculated. In a typical system, the chair has a period of oscillation of 0.901 s when empty. The spring constant is 606 N/m. When a certain astronaut sits in the chair, the period of oscillation increases to 2.37 s. Determine the mass of the astronaut. FIGURE P16.23
A simple pendulum has a length of 52.0 cm and makes 82.0 complete oscillations in 2.00 min. Find (a) the period of the pendulum and (b) the value of g at the location of the pendulum.
A block with mass m = 0.1 kg oscillates with amplitude .A = 0.1 in 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 tanking, (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 underdamped.
The top end of a spring is held fixed. A block is hung on the bottom end as in Figure OQ15.13a, and the frequency f of the oscillation of the system is measured. The block, a second identical block, and the spring are carried up in a space shuttle to Earth orbit. The two blocks are attached to the ends of the spring. The spring is compressed without making adjacent coils touch (Fig. OQ15.13b), and the system is released to oscillate while floating within the shuttle cabin (Fig. OQ15.13C). What is the frequency of oscillation for this system in terms of f? (a) f/2 (b) f/ 2 (c) f (d) 2/ (e) 2f
What is the length of a pendulum that has a period of 0.500 s?