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# Oscillation, Motion and Energy

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A loudspeaker diaphragm is oscillating in simple harmonic motion with a frequency of 461 Hz and a maximum displacement of 0.57 mm. What are the
(a) angular frequency,
(b) maximum speed, and
(c) magnitude of the maximum acceleration?

A 7.66 kg object on a horizontal frictionless surface is attached to a spring with k = 2460 N/m. The object is displaced from equilibrium 64.4 cm horizontally and given an initial velocity of 9.29 m/s back toward the equilibrium position. What are
(a) the motion's frequency (in Hz),
(b) the initial potential energy of the block-spring system,
(c) the initial kinetic energy, and (d) the motion's amplitude?

https://brainmass.com/physics/conservation-of-energy/physics-loudspeaker-diaphragm-oscillation-block-spring-system-s-motion-energy-309306

#### Solution Preview

Chapter 15, Problem 71
A loudspeaker diaphragm is oscillating in simple harmonic motion with a frequency of 461 Hz and a maximum displacement of 0.57 mm. What are the (a) angular frequency, (b) maximum speed, and (c) magnitude of the maximum acceleration?

Solution: A SHM can be described by the equation: y = Asin(ωt) = Asin(2Пν)t ........(1) where y = displacement of the object describing SHM, A = amplitude, ω = angular frequency, ν = frequency.

Given: Frequency of oscillations = ν = 461 Hz, Maximum displacement (amplitude) = A = 0.57 mm = 0.57/1000 = 57 x 10-5 m

a) Angular ...