University:
University of Houston
Course:
PHYS 1301 | College Physics I (lecture)
Academic year:

2022
Views:

183

Pages:

14
Author:

caitlinbright981p

13-5 Energy conservation in oscillatory motion This diagram shows how the energy transforms from potential to kinetic and back, while the total energy remains the same. Example The period of oscillation of an object in an ideal massspring system is 0.50 sec and the amplitude is 5.0 cm. What is the speed at the equilibrium point? Example continued Example The diaphragm of a speaker has a mass of 50.0 g and responds to a signal of 2.0 kHz by moving back and forth with an amplitude of 1.8×10−4m at that frequency. Example continued Example The displacement of an object in SHM is given by: Example continued 13-6 The pendulum A simple pendulum consists of a mass m (of negligible size) suspended by a string or rod of length L (and negligible mass). The angle it makes with the vertical varies with time as a sine or cosine. 13-6 The pendulum Looking at the forces on the pendulum bob, we see that the restoring force is proportional to sin θ, whereas the restoring force for a spring is proportional to the displacement (which is θ in this case). 13-6 The pendulum However, for small angles, sin θ and θ are approximately equal. 13-6 The pendulum Substituting θ for sin θ allows us to treat the pendulum in a mathematically identical way to the mass on a spring. Therefore, we find that the period of a pendulum depends only on the length of the string: Example A clock has a pendulum that performs one full swing every 1.0 sec. The object at the end of the string weighs 10.0 N. What is the length of the pendulum? Example The gravitational potential energy of a pendulum is U = mgy. Taking y = 0 at the lowest point of the swing, show that y = L(1-cosθ). 13-6 The pendulum A physical pendulum is a solid mass that oscillates around its center of mass, but cannot be modeled as a point mass suspended by a massless string. Examples:

Oscillations About Equilibrium CH13 Claudia 2

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