Simple Harmonic Oscillation: Solving for Period, Frequency, Energy, and Velocity

AI Thread Summary
To solve for the period, frequency, angular frequency, energy, and maximum velocity of a mass-spring system, start by calculating angular frequency using the formula ω = √(k/m), where k is the spring constant and m is the mass. The period can then be found using the relationship period = 2π/ω, and frequency is the inverse of the period. The energy in the system is calculated with E = 1/2 kx², where x is the compression distance. The maximum velocity occurs when the spring's potential energy is converted to kinetic energy at the equilibrium point. Understanding these relationships allows for the complete analysis of simple harmonic motion.
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Homework Statement


A block of mass 5 kg is attached to a spring of 2000N/m and compressed a distance of 0.6m. The spring is then released and oscillates.
a. what are the period, frequency, and angular frequency
b. what is the energy in this system
c. what is the maximum velocity


Homework Equations


period=1/frequency
d^2x/dt^2 + (k/m)x = 0
\omega= (2*pi)*frequency= 2pi/period= sqrt(k/m)
E= 1/2mv^2 + 1/2kx^2= 1/2kA^2


The Attempt at a Solution


I have not been able to attempt a solution because I do not know where to start. Please help.
 
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you have all your equations and all your variables needed to find your unknowns..

if omega = sqrt (K/m)
find omega

then you can find period and frequency, angular frequency from there.

Energy of a spring is defined as.. 1/2 kx^2
..find energy

max velocity is when potential spring energy = kinetic energy, (equilibrium point)
 

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