VDU_Physics_2_002  
Solved UniversityPhysics ProblemsPhysics 2. Energy in OscillationsJavier Montenegro Joo 

Energy in Oscillations 

[1]
An oscillator of mass m and frequency f, vibrates with SHM, with a
maximum amplitude A_{o}. Determine the amplitude of the
oscillator at the time when 2/3 of its total energy is: (a) potential
(b) kinetic. Solution .


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Algorithmic Art by Javier Montenegro Joo


[2] An oscillating spring (SHM) of mass m and frequency f_{o} has a total energy E_{o} Determine (a) Its maximum velocity (b) Its maximum amplitude. Solution.


[3]
A block on a frictionless horizontal table is attached to the extreme of
a 40cmlong spring, and negligible mass, whose other extreme remains
fixed by means of a nail in the tabletop. By applying 12 J the spring
is compressed down to 10 cm, wherefrom the block is released and
experiences a 25 m/s^{2 } maximum acceleration. Determine the
mass of the block (b) the elastic constant of the spring (c) the
oscillation frequency of the block.
Solution. The work done to compress the spring is stored as potential energy of the spring:


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[4] A spring of mass m_{o} vibrates with a SHM of frequency f_{o }. Determine: (a) The elastic constant k_{o} of the spring (b) The maximum amplitude of oscillation (c) The potential energy at the extreme of the oscillation (d) The kinetic energy when the spring passes by its equilibrium position. It is known that the total energy of the vibrating spring is (2 Pi^{2})^{1} Solution.


Physics Virtual Lab (PVL): Evolution of the energy in the Simple Harmonic Motion:
The PVL is a collection of 193 professional and highly interactive physics simulation modules, that can be used to learn and to teach physics. 

[5] (a) Determine the maximum speed attained by a 0.5 kg spring whose maximum amplitude of oscillation is 8 cm. (b) Calculate the speed of the coil when it is at 2.5 cm away of its equilibrium position. It has been observed that when the spring is placed vertical on the ground and a 5 kg sphere is placed on it, the spring shrinks 10 cm. Solution. First, the elastic constant of the spring must be calculated from the weight of the sphere placed on the vertical spring:


[6] A spring whose elastic constant is 100 N/m oscillates with simple harmonic motion (SHM) whose max amplitude is 5 cm. Determine the position of the coilspring when its speed is: (a) 25% of its max value (b) 50% of its max value. Solution. In this problem the value of the elastic constant of the spring is there just to bother the student; it plays no role in the solution.


