VDU_Physics_2_001  
Solved UniversityPhysics ProblemsPhysics 2. Oscillations  Simple Harmonic Motion (SHM)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:


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(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:


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(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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(6)
Two
pendulums ‘a’ and ‘b’ that are oscillating with simple harmonic motion
have lengths L_{b} = 3 L_{a} and, their maximum
oscillation amplitudes are Q_{a} and Q_{b , }
respectively (Q : angle theta). It is known that their maximum speeds
are such that V_{bmax} = 5 V_{amax} . Find the
relationship Q_{bmax }/ Q_{amax} Solution.


(7)
An oscillating spring coil passes through its equilibrium position every
4 s. Determine its mass taking into account that the spring is
compressed 2 cm when it is placed vertical on the floor and a block of
200 gr is put on top of it. Solution. During each oscillation, the spring goes twice through its equilibrium position, then


(8)
The motion of an oscillator is mathematically described by z(t) = A
Sin( 5 t + p ). Determine its maximum amplitude of oscillation and
its initial phase. It is known that its initial position and speed are
4 and 10, respectively. Solution .


(9) Two pendulums ‘a’ and ‘b’ that are oscillating with simple harmonic motion (SHM) have lengths L_{a } and L_{b} respectively, so that L_{b} = 3 L_{a} . Their maximum oscillation amplitudes are Q_{b }= 2.8867 Q_{a, } (where Q = angle theta). Find the relationship V_{bmax }/ V_{amax.} Solution.


