What Is the Maximum Velocity of an Object in Harmonic Motion?

[chazgurl4life]

An object with mass 3.5 kg is attached to a spring with spring stiffness constant k = 300 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s.

b) Calculate the maximum velocity attained by the object. [Hint: Use conservation of energy.]

so if i use E= 1/2mv^2=1/2KX^2
then-->.5(3.5 kg)(.55) ^2= 1.5(300 N/m)(.200) ^2

but what does that prove ? I don't think this is right

 

[Andrew Mason]

An object with mass 3.5 kg is attached to a spring with spring stiffness constant k = 300 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s.

b) Calculate the maximum velocity attained by the object. [Hint: Use conservation of energy.]

so if i use E= 1/2mv^2=1/2KX^2
then-->.5(3.5 kg)(.55) ^2= 1.5(300 N/m)(.200) ^2

but what does that prove ? I don't think this is right

You are right - your answer is not right.

Just add the kinetic and potential energy to find its total energy. Energy is conserved. So when potential energy = 0, kinetic energy = total energy. That is where it will have maximum speed.

AM

 

[neutrino]

When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s.

That piece of information let's you calculate the potential and kinetic energies (at the point .02m from equillibrium). With that you can calculate the total energy of the system(E = P+K). Now how is this connected to the maximum velocity the object can have?