Amplitude of horizontal mass-spring system

Click For Summary
SUMMARY

The discussion centers on calculating the amplitude (A) and spring constant (k) of a horizontal mass-spring system undergoing simple harmonic motion. Given parameters include a maximum velocity (Vmax) of 20 m/s, a force (F) of 10 N, and a mass (m) of 0.5 kg. The amplitude can be derived using Hooke's law and the relationship between maximum velocity and amplitude in simple harmonic motion. The position function x(t) = A cos(ωt) illustrates the sinusoidal nature of the motion, confirming that the amplitude represents the maximum displacement from the equilibrium position.

PREREQUISITES
  • Understanding of simple harmonic motion principles
  • Familiarity with Hooke's law
  • Knowledge of angular frequency (ω) calculations
  • Basic physics concepts related to force, mass, and acceleration
NEXT STEPS
  • Calculate the spring constant (k) using the formula k = F/x, where x is the amplitude.
  • Explore the relationship between maximum velocity and amplitude in simple harmonic motion.
  • Learn about angular frequency (ω) and its role in simple harmonic motion equations.
  • Review examples of mass-spring systems to reinforce understanding of amplitude and spring constant calculations.
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to clarify concepts related to mass-spring systems.

thatonenozz
Messages
2
Reaction score
0

Homework Statement



This is a horizontal mass spring system in a simple harmonic motion problem set.

Vmax = 20 m/s
F = 10 N
m = 0.5 kg

Find Amplitude (A) and spring constant (k)

Homework Equations


The Attempt at a Solution



I could not figure out a way to solve this problem, and the only thing i could come up with was that the amplitude is equal to the x distance stretched. If this is true, then i can solve it using Hooke's law and other equations, but I'm not too sure it works out like that. Any help would be greatly appreciated!
 
Physics news on Phys.org
You are correct. Remember that the hallmark of simple harmonic motion is a sinusoidal time dependence for position, e.g.

[tex]x(t) = A\ \text{cos}(\omega t)[/tex]

When [itex]t = 0[/itex], for instance, the position will be at its maximum value, which we call the amplitude of the motion.
 

Similar threads

Replies
5
Views
1K
  • · Replies 8 ·
Replies
8
Views
2K
Replies
3
Views
988
Replies
17
Views
2K
  • · Replies 1 ·
Replies
1
Views
8K
  • · Replies 5 ·
Replies
5
Views
1K
Replies
9
Views
4K
Replies
17
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
3
Views
1K