You are here:

Physics/Waves, physics

Advertisement


Question
I am having difficulty answering these theoretical questions. Any help would be greatly appreciated.

      In the following physical systems that undergo simple harmonic motion, state which physical quantity or quantities you think will influence the period of motion and in what manner. Briefly justify your predictions using physical arguments rather than equations.
a. mass-spring system (oscillating horizontally on a frictionless surface)
b. simple pendulum

     In an ideal mass-spring system (oscillating horizontally on a frictionless surface), the total energy is conserved. What types of energy are involved?

What is the expression for total energy
a. When the mass is at maximum displacement (x = A) in terms of A?
b. When the mass is passing through equilibrium (x = 0) in terms of v_max?

   Using the fact that energy is conserved and the expressions found in the previous part, find an expression for maximum speed in terms of m, k and/or A.

Answer
Hello Nick,

>In the following physical systems that undergo simple harmonic motion,
>state which physical quantity or quantities you think will influence
>the period of motion and in what manner. Briefly justify your predictions
>using physical arguments rather than equations.
>a. mass-spring system (oscillating horizontally on a frictionless surface)

Greater spring constant, k, will decrease the period. Greater mass, m, will increase the period. In the definition of a simple harmonic oscillator, it is said that the restoring force is proportional to the displacement from the equilibrium position. A higher value of k increases the force. The acceleration increases with increasing force but decreases with increasing m.

>b. simple pendulum

Increasing pendulum rod length increases the period. In a pendulum, for a given displacement from equilibrium, the restoring force is proportional to the elevation gained from the displacement. Longer rods give less elevation for a given displacement, therefore less restoring force. Mass does not change period for the same reason that different mass balls fall at the same rate during free fall. A greater value of g also decreases period -- makes clocks run faster.

>In an ideal mass-spring system (oscillating horizontally on a
>frictionless surface), the total energy is conserved. What types
>of energy are involved?

Kinetic energy and spring potential energy

>What is the expression for total energy
>a. When the mass is at maximum displacement (x = A) in terms of A?

total energy = spring potential energy

>b. When the mass is passing through equilibrium (x = 0) in terms
>of v_max?

total energy = kinetic energy

>Using the fact that energy is conserved and the expressions found
>in the previous part, find an expression for maximum speed in
>terms of m, k and/or A.

max spring potential energy = max kinetic energy
(1/2)*k*A^2 = (1/2)*m*Vmax^2
Vmax^2 = k*A^2 / m
Vmax = A*sqrt(k/m)

I hoep this helps,
Steve

Physics

All Answers


Answers by Expert:


Ask Experts

Volunteer


Steve Johnson

Expertise

I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

Experience

I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

Education/Credentials
BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University

©2016 About.com. All rights reserved.