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

The conversation discusses a block attached to a spring and its oscillations after being released. The period, frequency, and angular frequency are unknown and can be found using the given equations. The energy in the system can be calculated using the equation for spring energy. The maximum velocity can be determined when the potential spring energy is equal to the kinetic energy at the equilibrium point. In summary, the period, frequency, and angular frequency can be found using the given equations, the energy in the system can be calculated using the equation for spring energy, and the maximum velocity can be determined at the equilibrium point.
  • #1
jmm21242
2
0

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
[tex]\omega[/tex]= (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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  • #2
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)
 

What is simple harmonic oscillation?

Simple harmonic oscillation is a type of periodic motion where the displacement of an object from its equilibrium position is proportional to the force acting on it. This means that the object will oscillate back and forth between two points with a constant period and amplitude.

What are the factors that affect simple harmonic oscillation?

The factors that affect simple harmonic oscillation include the mass of the object, the spring constant of the system, and the amplitude of the oscillation. The period of the oscillation is also affected by these factors, as well as the initial displacement of the object.

How is simple harmonic oscillation different from other types of oscillation?

Simple harmonic oscillation is different from other types of oscillation because it follows a specific mathematical pattern known as a sine wave. This wave is characterized by its amplitude, wavelength, and frequency, which remain constant throughout the oscillation.

What are some real-life examples of simple harmonic oscillation?

Some real-life examples of simple harmonic oscillation include the motion of a pendulum, the vibrations of a guitar string, and the movement of a mass on a spring. These systems exhibit simple harmonic motion because they follow the same mathematical pattern and have a constant period and amplitude.

What is the significance of simple harmonic oscillation in science and engineering?

Simple harmonic oscillation is significant in science and engineering because it helps us understand and predict the behavior of many physical systems. It is also used in various applications, such as in timekeeping devices, musical instruments, and shock absorbers, to name a few.

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