What Are the Amplitude and Period of the Mass-Spring System?

Click For Summary
SUMMARY

The discussion focuses on calculating the amplitude and period of a mass-spring system with a spring constant of k=74 N/m and a mass of 490g. The user employs the formula F = -kx and attempts to express displacement as x = A cos(ωt), where ω is the angular frequency. To find the amplitude A, the user is advised to determine ω using the formula ω = √(k/m) and to recognize that at maximum displacement, the velocity is zero, which simplifies the calculations.

PREREQUISITES
  • Understanding of Hooke's Law and spring constant (k)
  • Knowledge of angular frequency (ω) in oscillatory motion
  • Familiarity with the concepts of amplitude and period in harmonic motion
  • Basic algebra for manipulating equations involving trigonometric functions
NEXT STEPS
  • Calculate the angular frequency ω using the formula ω = √(k/m)
  • Determine the period T of the mass-spring system using T = 2π/ω
  • Explore the relationship between maximum displacement and velocity in harmonic motion
  • Investigate the effects of varying the mass and spring constant on the system's behavior
USEFUL FOR

Students and educators in physics, mechanical engineers, and anyone studying oscillatory systems and harmonic motion.

teenholiday
Messages
4
Reaction score
0
A massless sping of spring constant k=74 N/m is hanging from the ceiling. A 490g mass is hooked onto the unstretched spring and allowed to drop. Find the amplitude and the period of the resulting motion.

Attempt:
F= -kx

x= A cos (wt)
w = sqrt(k/m) t

I'm trying to solve for A, but how do I get rid of the t variable?


Thanks
 
Physics news on Phys.org
Find [itex]\omega[/itex] and you could use the fact that at max displacement from the equilibrium posistion, velocty=0.
 

Similar threads

Sliding block hits and compresses a spring
  • · Replies 5 ·
Replies
5
Views
1K
Derivation of the oscillation period for a vertical mass-spring system
  • · Replies 9 ·
Replies
9
Views
4K
Stretching of a rotating spring
  • · Replies 8 ·
Replies
8
Views
2K
Mass atop four springs with external input: Reduce vibration amplitude by factor of ten
  • · Replies 3 ·
Replies
3
Views
1K
What is the Period of Oscillation for a Spring Cut to One-Third Its Length?
  • · Replies 3 ·
Replies
3
Views
1K
Time period of SHM & Energy conservation in pulley-spring-block system
  • · Replies 24 ·
Replies
24
Views
4K
Force transmitted to a block in viscous fluid through a spring, cord, and pulley
  • · Replies 6 ·
Replies
6
Views
1K
Two spring-coupled masses in an electric field (one of the masses is charged)
  • · Replies 1 ·
Replies
1
Views
1K
Estimating damped harmonic oscillator parameters from this plot of the oscillations
  • · Replies 9 ·
Replies
9
Views
2K
Absolute motion analysis of pulley-spring system
  • · Replies 10 ·
Replies
10
Views
1K