I need help with these questions thanks beforehand! 1) Write the equation for th

Question

I need help with these questions thanks beforehand!
1) Write the equation for the position in a SHM.

2) Use the equation of the position to find the equation of the velocity in a SHM.  

3) Use the equation of the position to find the potential elastic energy in a SHM.

4) Use the equation of the velocity in a SHM to find the kinetic energy in SHM.

5) Write an equation to show the relationship between potential elastic energy, kinetic energy and the total mechanical energy of a simple harmonic oscillator.  

Explanation / Answer

The general solution can also be written more compactly as

y(t)= A cos(?t - ?)

2. Differentiating once with respect to time, we obtain the velocity.(The derivative ofcos x = -sin x)

  v = y'(t)= - ?A sin(?t - ?)

3. PE(t) = 1/2k [A cos(?t - ?)]^2

4. kE = 1/2 *m* [- ?A sin(?t - ?)]^2

5. here k= m*w^2

therfore total energy= KE+PE = 1/2*K*A^2

The total energy remains constant because there are no losses to friction, heat or air resistance.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects