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Solved University-Physics Problems

Physics 2.- Oscillations - Simple Harmonic Motion

Javier Montenegro Joo

jmj@VirtualDynamics.Org

 

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Oscillations - Simple Harmonic Motion (SHM)

 
 

(1) The vibrations of a vertical spring are mathematically modeled by

 

Determine: (a) the initial values of displacement, velocity and acceleration. (b) The maximum values of displacement, velocity and acceleration.       

Solution

First of all get mathematical expressions for displacement, velocity and acceleration:

 

 

     
  (2) The horizontal oscillations of a small ball are mathematically represented by

Determine: (a) the initial values of displacement, velocity and acceleration. (b) The maximum values of displacement, velocity and acceleration.       

Solution

First of all get mathematical expressions for displacement, velocity and acceleration:

 
 

 

 
 

 (3) The vibrations of a pendulum oscillating with simple harmonic motion (SHM) are represented by

                                        

Determine:   (a) Initial amplitude   (b) Initial velocity   (c) Initial acceleration (d) length of pendulum.  

Solution

In order to identify the terms in the given equation compare it with that of the pendulum oscillating with Simple Harmonic Motion (SHM) given by:

 
     
  (4) The Simple Harmonic Motion (SHM) oscillations of a spring are represented in the MKSC system by

 

Determine: (a)  Maximum amplitude  (b) Maximum velocity (c) Maximum acceleration (d) Initial phase   (e) frequency.      

Solution

By comparing the given equation with that of a spring oscillating with Simple Harmonic Motion (SHM):

 
     
  (5) When a 2.0 kg block is hung from a vertical spring, this stretches 20 cm.  Later this spring is placed horizontally on a frictionless floor with one of its extremes against the wall and, a 5 kg block is attached to its free extreme. Determine the period and the angular frequency of the oscillation of the system when it is compressed against the wall and released. 

 Solution.-

The data about the vertical spring is used to calculate the elastic constant of the spring from Hooke’s law:

 
     
     
 

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