Select the suitable conclusions from the options given1. The period of a simple pendulum depends on the2. In order to double the period of the simple pendulum, length of the simple pendulum should be increased by3. The time period of the simple pendulum is independent of• and the Select the suitable conclusions from the options given1. The period of a simple pendulum depends on the2. In order to double the period of the simple penduould be increased bylength of the cord4 timesmass of boband the3. The time period of the simple pendulum is indepe amplitude of oscillationsdoubledsquare of the length of the cordincreasesdecreasesfrequency3 timesFoundations

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Description: Select the suitable conclusions from the options given1. The period of a simple pendulum depends on the2. In order to double the period of the simple pendulum, length of the simple pendulum should be increased by3. The time period of the simple pend

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1. The period of a simple pendulum depends on th- 2. In order to double the period of the simple pend 3. The time period of the simple pendulum is indep

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter3: Oscillations

Section: Chapter Questions

Problem 3.8P

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A simple harmonic oscillator has amplitude A and period T. Find the minimum time required for its position to change from x = A to x = A/2 in terms of the period T.
The equations listed in Table 2.2 give position as a function of time, velocity as a function of time, and velocity as a function of position for an object moving in a straight line with constant acceleration. The quantity vxi appears in every equation. (a) Do any of these equations apply to an object moving in a straight line with simple harmonic motion? (b) Using a similar format, make a table of equations describing simple harmonic motion. Include equations giving acceleration as a function of time and acceleration as a function of position. State the equations in such a form that they apply equally to a blockspring system, to a pendulum, and to other vibrating systems. (c) What quantity appears in every equation?
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).
An undamped driven harmonic oscillator satisfies the equation of motion m(d2x/dt2+ 02x) = F(t). The driving force F(t) = F0 sin(t) is switched on at t= 0. (a) Find x(t) for t 0 for the initial conditions x = 0 and v = 0 at t = 0. (b) Find x(t) for = 0 by taking the limit 0 in your result for part (a). Sketch your result for x(t). Hint: In part (a) look for a particular solution of the differential equation of the form x = A sin(t) and determine A. Add the solution of the homogeneous equation to this to obtain the general solution of the inhomogeneous equation.
(a) If frequency is not constant for some oscillation, can the oscillation be simple harmonic motion? (b) Can you mink of any examples of harmonic motion where the frequency may depend on the amplitude?
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?
Allow the motion in the preceding problem to take place in a resisting medium. After oscillating for 10 s, the maximum amplitude decreases to half the initial value. Calculate (a) the damping parameter β, (b) the frequency υ1 (compare with the undamped frequency υ0), and (c) the decrement of the motion.
A simple pendulum has mass 1.20 kg and length 0.700 m. (a) What is the period of the pendulum near the surface of Earth? (b) If the same mass is attached to a spring, what spring constant would result in the period of motion found in part (a)?
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?
Obtain an expression for the fraction of a complete period that a simple harmonic oscillator spends within a small interval Δx at a position x. Sketch curves of this function versus x for several different amplitudes. Discuss the physical significance of the results. Comment on the areas under the various curves.
In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression x=5.00cos(2t+6) where x is in centimeters and t is in seconds. At t = 0, find (a) the position of the piston, (b) its velocity, and (c) its acceleration. Find (d) the period and (e) the amplitude of the motion.
Suppose you have a 0.750-kg object on a horizontal surface connected to a spring that has a force constant of 150 N/m. There is simple friction between the object and surface with a static coefficient of friction s=0.100 . (a) How far can the spring be stretched without moving the mass? (b) If the object is set into oscillation with an amplitude twice the distance found in part (a), and the kinetic coefficient of friction is k=0.0850 , what total distance does it travel before stopping? Assume it starts at the maximum amplitude.