Simple Harmonic Motion and speed of mass

Which is what you are doing here, with the differential equation and the initial conditions. The reason you can't just take a number from there is that the motion is periodic, so you can't say "it's 5 m/s" because it's not always 5 m/s, it's 5 m/s at one point in time.In summary, the conversation discusses the calculation of the speed of a mass in a mass-spring system when the kinetic energy and potential energy are equal. The solution involves solving a differential equation and setting initial conditions to find the time and speed at which this occurs. It is not possible to solve for a single number, as the motion is periodic.
  • #1
e^(i Pi)+1=0
247
1

Homework Statement


[/B]
A mass-spring system is oscillating with an amplitude of 10.0 cm. What is the speed of the mass at a location where the kinetic energy of the mass and the potential energy of the spring are equal?

I want to know if it's possible to solve for just a number, that is, not in terms of k and m. Also if my answer is right as it is. Thanks.

Homework Equations

The Attempt at a Solution


[/B]
Force equals ma and also -kx
ma = -kx
ma+kx = 0
x''+(k/m)x = 0

Solve the differential equation, set x(0) = 0 and set the amplitude to 0.1 (in meters) to yield

x(t) = 0.1sin(√[k/m]t)

Differentiate to find v(t) and sub them into the equation

(1/2)mv2 = (1/2)kx2

I find t = π/4 and v(π/4) = -0.05√(2k/m)
 
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  • #2
e^(i Pi)+1=0 said:
I want to know if it's possible to solve for just a number
No. Dimensional analysis: you are given a length, and you want a speed; you need a velocity or an acceleration etc. to connect those two dimensions.
 

1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion where an object moves back and forth around a central equilibrium point, with a restoring force proportional to the displacement from the equilibrium point.

2. What factors affect the speed of mass in simple harmonic motion?

The speed of mass in simple harmonic motion is affected by the amplitude of the motion, the mass of the object, and the spring constant of the system.

3. How can the speed of mass be calculated in simple harmonic motion?

The speed of mass in simple harmonic motion can be calculated using the equation v = ω√(A^2-x^2), where v is the speed, ω is the angular frequency, A is the amplitude, and x is the displacement from the equilibrium point.

4. Is the speed of mass constant in simple harmonic motion?

No, the speed of mass in simple harmonic motion is not constant. It varies throughout the motion, with the highest speed at the equilibrium point and decreasing as the object moves away from the equilibrium point.

5. How is simple harmonic motion related to energy?

Simple harmonic motion involves the exchange of potential and kinetic energy. As the object moves towards the equilibrium point, potential energy is converted into kinetic energy. As it moves away from the equilibrium point, kinetic energy is converted back into potential energy. The total energy of the system remains constant.

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