A 1.5-m length pendulum is displaced byan initial angle e = +6° and released fromrest. If the angular position is given as acosine function, E(t) = Omax cos(wt+p),then the angular velocity as a functionof time is: (Take g = 10 m/s?)e'(t) = 0.24 sin(2.6t+r/2)O e'(t) = -0.27 sin(2.6t)O e'(t) = -0.24 sin(2.3t+T)e'(t) = -0.27 sin(2.6t+n)O e'(t) = 0.27 sin(2.6t-t/3)

Name: A 1.5-m length pendulum is displaced byan initial angle e = +6° and r
Uploaded: 2024-03-20T06:58:04.000Z
Channel: Bartleby
Description: A 1.5-m length pendulum is displaced byan initial angle e = +6° and released fromrest. If the angular position is given as acosine function, E(t) = Omax cos(wt+p),then the angular velocity as a functionof time is: (Take g = 10 m/s?)e'(t) = 0.24 sin(

Frequency of oscillations is proportional to acceleration due to gravity and inversely to length for…

Science

Physics

A 1.5-m length pendulum is displaced by an initial angle = +6° and released from rest. If the angular position is given as a cosine function, e(t) = max cos(wt+q), then the angular velocity as a function of time is: (Take g = 10 m/s²) O 0'(t) = 0.24 sin(2.6t+π/2) O 0¹(t) = -0.27 sin(2.6t) O 0'(t) = -0.24 sin(2.3t+n) O 0¹(t) = -0.27 sin(2.6t+à) O 0'(t) = 0.27 sin(2.6t-π/3)

A 1.5-m length pendulum is displaced by an initial angle = +6° and released from rest. If the angular position is given as a cosine function, e(t) = max cos(wt+q), then the angular velocity as a function of time is: (Take g = 10 m/s²) O 0'(t) = 0.24 sin(2.6t+π/2) O 0¹(t) = -0.27 sin(2.6t) O 0'(t) = -0.24 sin(2.3t+n) O 0¹(t) = -0.27 sin(2.6t+à) O 0'(t) = 0.27 sin(2.6t-π/3)

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 3.31P

See similar textbooks

Similar questions

Give an example of a simple harmonic oscillator, specifically noting how its frequency is independent of amplitude.
Refer to the problem of the two coupled oscillators discussed in Section 12.2. Show that the total energy of the system is constant. (Calculate the kinetic energy of each of the particles and the potential energy stored in each of the three springs, and sum the results.) Notice that the kinetic and potential energy terms that have 12 as a coefficient depend on C1 and 2 but not on C2 or 2. Why is such a result to be expected?
Show that, if a driven oscillator is only lightly damped and driven near resonance, the Q of the system is approximately Q2(TotalenergyEnergylossduringoneperiod)
Show that the time rate of change of mechanical energy for a damped, undriven oscillator is given by dE/dt = bv2 and hence is always negative. To do so, differentiate the expression for the mechanical energy of an oscillator, E=12mv2+12kx2, and use Equation 12.28.
Can this analogy of SHM to circular motion be carried out with an object oscillating on a spring vertically hung from the ceiling? Why or why not? If given the choice, would you prefer to use a sine function or a cosine function to model the motion?
Check Your Understanding Identify one way you could decrease the maximum velocity of a simple harmonic oscillator.
Do you think there is any harmonic motion in the physical world that is not damped harmonic motion? Try to make a list of five examples of undamped harmonic motion and damped harmonic motion. Which list was easier to make?
Check Your Understanding Why are completely undamped harmonic oscillators so rare?
Check Your Understanding Identify an object that undergoes uniform circular motion. Describe how you could trace the SHM of this object.
We do not need the analogy in Equation 16.30 to write expressions for the translational displacement of a pendulum bob along the circular arc s(t), translational speed v(t), and translational acceleration a(t). Show that they are given by s(t) = smax cos (smpt + ) v(t) = vmax sin (smpt + ) a(t) = amax cos(smpt + ) respectively, where smax = max with being the length of the pendulum, vmax = smax smp, and amax = smax smp2.
Most harmonic oscillators are damped and, if undriven, eventually come to a stop. Why?
Consider a graphical representation (Fig. 12.3) of simple harmonic motion as described mathematically in Equation 12.6. When the particle is at point on the graph, what can you say about its position and velocity? (a) The position and velocity are both positive. (b) The position and velocity are both negative. (c) The position is positive, and the velocity is zero. (d) The position is negative, and the velocity is zero. (e) The position is positive, and the velocity is negative. (f) The position is negative, and the velocity is positive. Figure 12.3 (Quick Quiz 12.2) An xt graph for a particle undergoing simple harmonic motion. At a particular time, the particles position is indicated by in the graph.