Finding Amplitude of Oscillation for a Spring-Mass System

In summary, the problem involves a 100 g ball attached to a spring with spring constant 2.5 N/m oscillating horizontally on a frictionless table. The velocity of the ball is given as 20 cm/s when x = -5.0 cm. The relevant equations used to solve for the amplitude of the oscillation are x = Acos(ωt +φ ) and V= -ωAcos(ωt +φ ), where ω = √(k/m) and phi is the phase angle, a constant. However, the expression V= -ωAcos(ωt +φ ) is incorrect and needs to be checked.
  • #1
05holtel
52
0

Homework Statement



A 100 g ball is attached to a spring with spring constant 2.5 N/m oscillates horizontally on a frictionless table. Its velocity is 20 cm/s when x = -5.0 cm. What is the amplitude of the oscillation?


Homework Equations



x = Acos(ωt +φ )
V= -ωAcos(ωt +φ )

The Attempt at a Solution



ω = Square root (k/m) = 5 rad/s
-0.05 = Acos(ωt +φ )
0.2 = -ωAcos(ωt +φ )

Not sure how to solve for A
 
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  • #2
To begin, you need to go back to your (relevant) equations. You have a differentiation mistake there that makes lit impossible to proceed correctly. Get this straight, and the solution for A should become evident using the Pythagorean trig identity.
 
  • #3
can I get φ clarified is it a constant? I know Acos(ωt+kx) is standard for traveling wave, however I am not certain of SHO for a spring what φ is.
 
  • #4
When an expression is written in that form, the implication is that phi is the phase angle, a constant. Evidently that was not explicitly stated, and it rarely is, but that is usually what is intended.
 
  • #5
V= -ωAcos(ωt +φ )

This expression is wrong. Check it.
 

FAQ: Finding Amplitude of Oscillation for a Spring-Mass System

1. What is the amplitude of oscillation?

The amplitude of oscillation is the maximum displacement of a particle or object from its equilibrium position during one cycle of oscillation. It is a measure of the strength or intensity of the oscillation.

2. How is the amplitude of oscillation related to frequency and period?

The amplitude of oscillation is inversely proportional to both the frequency and period of the oscillation. This means that as the frequency or period increases, the amplitude decreases, and vice versa.

3. What factors affect the amplitude of oscillation?

The amplitude of oscillation is affected by the properties of the oscillating system, such as its mass, stiffness, and damping. It is also influenced by external forces acting on the system, such as friction or air resistance.

4. Can the amplitude of oscillation change over time?

Yes, the amplitude of oscillation can change over time due to various factors. For example, in a damped oscillation, the amplitude decreases over time due to the dissipation of energy. In an undamped oscillation, the amplitude can remain constant if there are no external forces acting on the system.

5. How is the amplitude of oscillation measured?

The amplitude of oscillation can be measured by taking the maximum displacement of the oscillating object or particle from its equilibrium position. This can be done using a ruler, tape measure, or other measuring tools depending on the size and type of oscillating system.

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