When the displacement in simple harmonic motion is half of the amplitude, A, wha

Question

When the displacement in simple harmonic motion is half of the amplitude, A, what fraction of the total energy is: Potential? Kinetic? At what displacement, in terms of amplitude, are the potential and kinetic energy of the system equal? Shake tables are commonly used to test how well objects will withstand vibrations. The object sits on a table that vibrates and the vibration amplitude is increased until the object breaks. Consider a simple object (a block) that sits on a vibrating table where the vibrations are described by SHM at a frequency of 10 Hz (see picture above). If the coefficient of static friction between the table and block is 0.7, what would be the maximum amplitude of oscillations before the block breaks loose?

Explanation / Answer

3.

a)

Total Energy

E=(1/2)KA2

Given X=(1/2)A

Potential energy

U=(1/2)KX2 =(1/2)K[(1/2)A]2

U=(1/4)[(1/2)KA2]

U=(1/4)E

b)

Kinetic energy

K=E-U =E-(1/4)E

K=(3/4)E

c)

Given

U=(1/2)E

(1/2)KX2 =(1/2)[(1/2)KA2]

X=sqrt[A2/2] =A/sqrt[2]

X=0.707A

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