How does the mass on a horizontal spring behave?

  • Thread starter Thread starter mattmannmf
  • Start date Start date
  • Tags Tags
    Mass Spring
Click For Summary
SUMMARY

The discussion focuses on the oscillatory behavior of a 53 gram mass attached to a massless spring, described by the equation y(t) = 1.2*sin(3.1415*t). The spring constant can be calculated using the formula k = mω², where m is the mass in kilograms and ω is the angular frequency. The total mechanical energy, maximum kinetic energy, and maximum velocity of the mass can be derived from the amplitude and angular frequency, leading to specific numerical solutions for each query.

PREREQUISITES
  • Understanding of harmonic motion and oscillation principles
  • Familiarity with spring constant calculations
  • Knowledge of mechanical energy conservation in oscillatory systems
  • Ability to apply trigonometric functions in physical contexts
NEXT STEPS
  • Calculate the spring constant using k = mω² for the given mass and angular frequency
  • Determine the total mechanical energy using E = 0.5*k*A²
  • Find the maximum kinetic energy using KE_max = 0.5*m*v_max²
  • Analyze the maximum velocity using v_max = Aω
USEFUL FOR

Students and educators in physics, mechanical engineers, and anyone interested in understanding the dynamics of mass-spring systems and harmonic motion.

mattmannmf
Messages
170
Reaction score
0
A 53 gram mass is attached to a massless spring and allowed to oscillate around an equilibrium according to:
y(t) = 1.2*sin( 3.1415*t ) where y is measured in meters and t in seconds

(a) What is the spring constant in N/m ?

(b) What is the total Mechanical Energy in the mass/spring system?

(c) What is the maximum Kinetic Energy of the mass?

(d) What is the maximum velocity of the mass in m/s ?
 
Physics news on Phys.org
What are your thoughts on how to approach it?
 

Similar threads

Distribution of Energy when work is done on a system of 2 masses connected by a spring
  • · Replies 17 ·
Replies
17
Views
2K
Why can we move the spring with constant speed when we apply a force?
  • · Replies 29 ·
Replies
29
Views
3K
Two spring-coupled masses in an electric field (one of the masses is charged)
  • · Replies 1 ·
Replies
1
Views
1K
Initial velocity of bird landing on horizontal wire modeled as spring
  • · Replies 7 ·
Replies
7
Views
1K
How to Calculate Amplitude Decrease in Damped Harmonic Motion After 10 Cycles?
  • · Replies 3 ·
Replies
3
Views
848
Question about springs and rotational/translational energy
  • · Replies 4 ·
Replies
4
Views
2K
What happens when the maximum is exceeded in the Mass-Spring System?
  • · Replies 27 ·
Replies
27
Views
3K
A block of mass m is dropped onto the top of a vertical spring....
  • · Replies 8 ·
Replies
8
Views
6K
Time period of SHM & Energy conservation in pulley-spring-block system
  • · Replies 24 ·
Replies
24
Views
4K
How to solve a differential equation for a mass-spring oscillator?
  • · Replies 2 ·
Replies
2
Views
2K