Energy in simple harmonic motion
A 2.90 kg object oscillates with simple harmonic motion on a spring of force constant 600 N/m. The maximum speed is 0.800 m/s.
A) What is the total energy of the object and the spring?
B) What is the maximum amplitude of the oscillation?
Given that
The mass of the object (m) =2.90kg
The spring force constant (k) =600N/m
The maximum speed is(vmax) = 0.800 m/s
a)
The total energy of the object and the spring is given by
TE =(1/2)mvmax2+(1/2)kx2
We know that when the velocity is maximum then the potential energy is zero then total energy is
TE =E =(1/2)mvmax2 =0.5*2.90*(0.800)2 =0.928J
b)
There will be maximum amplitude , when the kinetic energy is minimum then
The maximum amplitude of the oscillation is given by
TE =E =(1/2)kx2
where x is the amplitude then
E =(1/2)kx2
x =Sqrt(2E/k) =Sqrt(2*0.928J/600N/m) =0.0556m
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