Simple Harmonic Motion for a block-spring system

In summary, the conversation discusses finding the ratio of kinetic energy to potential energy in a block-spring system in SHM, with a given phase angle and position equation. The solution involves using the equations for potential and kinetic energy and setting the calculator to radians for accuracy.
  • #1
obxer22
4
0

Homework Statement



If the phase angle for a block-spring system in SHM is π/5 rad and the block's position is given x = xm cos(ωt + phi), what is the ratio of the kinetic energy to the potential energy at time t = 0?

Homework Equations



PE = (1/2)*k*[(max amplitude)^2]*cos^2(ωt + phi)
KE = (1/2)*k*[(max amplitude)^2]*sin^2(ωt + phi)

Solve for KE/PE in that form.

The Attempt at a Solution



I took KE and divided by PE, giving sin^2(phi)/cos^2(phi). Plugging in pi/5 for phi gives us 1.20253316E-4/.99987974669. However, the system is saying this is wrong . I do believe that I solved for KE/PE correctly. Any help would be much appreciated. Thanks very much!
 
Physics news on Phys.org
  • #2
Have you set your calculator to RAD? pi/5 is in radians.

ehild
 
  • #3
I knew I was doing it right! my calculator was in degrees...i hate it when that happens...thanks for helping me figure that out!
 

Related to Simple Harmonic Motion for a block-spring system

1. What is Simple Harmonic Motion?

Simple Harmonic Motion is a type of periodic motion where a body moves back and forth around an equilibrium point, with a force that is directly proportional to the displacement from the equilibrium point and acts in the opposite direction of the displacement.

2. What is a block-spring system?

A block-spring system is a physical system consisting of a mass (or block) attached to a spring. The spring provides the restoring force that causes the block to undergo Simple Harmonic Motion.

3. What is the equation for Simple Harmonic Motion in a block-spring system?

The equation for Simple Harmonic Motion in a block-spring system is x(t) = A*cos(ω*t + φ), where x is the displacement of the block from its equilibrium point, A is the amplitude of the motion, ω is the angular frequency, and φ is the phase angle.

4. How does the mass of the block affect Simple Harmonic Motion in a block-spring system?

The mass of the block does not affect the period or frequency of Simple Harmonic Motion, but it does affect the amplitude. A larger mass will result in a smaller amplitude, while a smaller mass will result in a larger amplitude.

5. What factors can affect the period of Simple Harmonic Motion in a block-spring system?

The period of Simple Harmonic Motion can be affected by the mass of the block, the spring constant of the spring, and the amplitude of the motion. It is also affected by any external forces acting on the system, such as friction or air resistance.

Similar threads

Position and acceleration in simple harmonic motion given velocity
    • Introductory Physics Homework Help
Replies
16
Views
433
How to prove that motion is periodic but not simple harmonic?
    • Introductory Physics Homework Help
2
Replies
51
Views
2K
Time period of SHM & Energy conservation in pulley-spring-block system
    • Introductory Physics Homework Help
Replies
24
Views
1K
Pan suspended by a spring (Energy + SHM)
    • Introductory Physics Homework Help
Replies
20
Views
2K
Harmonic Motion of a Mass between two springs
    • Introductory Physics Homework Help
Replies
7
Views
2K
Moment of inertia problem involving a cylinder rolling down an incline
    • Introductory Physics Homework Help
Replies
11
Views
1K
Simple Harmonic Motion and Energy Problem
    • Introductory Physics Homework Help
Replies
16
Views
2K
What is the max amplitude before the sand particles slip off the vibrating plate?
    • Introductory Physics Homework Help
Replies
13
Views
343
Kinetic Energy from a Simple Harmonic motion and spring
    • Introductory Physics Homework Help
Replies
7
Views
2K
Zero Amplitude Damped Simple Harmonic Motion with k=0.7s^-1 and f=3Hz
    • Introductory Physics Homework Help
Replies
5
Views
867

Hot Threads

Recent Insights

Back
Top