An object-spring system moving with simple harmonic motion has an amplitude A .

Question

An object-spring system moving with simple harmonic motion has an amplitude A.

x = An object-spring system moving with simple harmonic motion has an amplitude A. What is the total energy of the system in terms of k and A only? Suppose at a certain instant the kinetic energy is twice the elastic potential energy. Write an equation describing this situation, using only the variables for the mass m, velocity v, spring constant k, and position x. Using the results of parts (a) and (b) and the conservation of energy equation, find the positions x of the object when its kinetic energy equals twice the potential energy stored in the spring.

Explanation / Answer

a)0.5*k*A^2

b)

elsastic potential energy=0.5*k*x^2

where x is the displacement

if speed at this point of time is v.

then 0.5*m*v^2=2*0.5*k*x^2

so v=x*sqrt(2*k/m)

now total eenrgy is constant.

so 0.5*m*v^2+0.5*k*x^2=0.5*k*A^2

so 3*0.5*k*x^2=0.5*k*A^2

x=A/sqrt(3)

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