Oscillating velocities, and energy

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SUMMARY

The discussion focuses on a physics problem involving a 0.40 kg mass oscillating on a spring with a frequency of 2.9 Hz and an amplitude of 0.20 m. The participant successfully calculated the spring constant (k) as 132.81 N/m using the formula k = 4π²m/T², where T is the period derived from the frequency. The participant seeks guidance on applying energy equations to determine the velocity at the equilibrium point and at a displacement of 0.10 m from equilibrium, as well as the total energy of the system.

PREREQUISITES
  • Understanding of simple harmonic motion (SHM)
  • Knowledge of spring constant calculations
  • Familiarity with kinetic and potential energy equations in oscillatory systems
  • Ability to manipulate trigonometric functions for motion equations
NEXT STEPS
  • Learn how to calculate kinetic energy (KE) and potential energy (PE) in oscillating systems
  • Study the derivation of the total mechanical energy in simple harmonic motion
  • Explore the equations of motion for oscillating systems, particularly using sine and cosine functions
  • Investigate the relationship between frequency, period, and angular frequency in SHM
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to clarify concepts related to energy in oscillating systems.

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Homework Statement


A 0.40- kg mass at the end of a spring oscillates 2.9 times per second with an amplitude of 0.20m.
a)Determine the magnitude of the velocity when it passes the equilibrium point.
b)Determine the magnitude of the velocity when it is 0.10 from equilibrium.
c)Determine the total energy of the system.
d)Determine the equation describing the motion of the mass, assuming that at = 0, was a maximum and that in seconds.
1- (0.4cm)cos18t
2- (0.4cm)sin18t
3- (0.2cm)sin18t
4- (0.2cm)cos18t

The Attempt at a Solution


maybe someone can help me start heading in the right direction. I am not really that sure where to start, or what equation to start with.

i calculated the k (spring constant) by manipulating the formula T^2=4π^2m/k to k=4π^2m/T^2. using m=.4 kg, frequency=2.9→period=1/2.9=.3448. so i got k=132.81 N/m.

im thinking the energy equations are supposed to be used for parts a,b due to the way part c is worded, but i can't see how the given information relates to the oscillating energy equations.
 
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im thinking the energy equations are supposed to be used for parts a,b due to the way part c is worded, but i can't see how the given information relates to the oscillating energy equations.

correct.


Find out the variations of Kinetic Energy and Potential Energy.
 

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