VDU_Physics_2_002

## Physics 2.- Energy in Oscillations

Javier Montenegro Joo

jmj@VirtualDynamicsSoft.com

## Energy in Oscillations

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

Solution .-

Algorithmic Art by Javier Montenegro Joo

[2] An oscillating spring (SHM) of mass m and frequency  fo   has a total energy  Eo  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 40cm-long 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/s2  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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With the module dealing with the reflection of circular waves, the user selects the wavelength and the position of the wave source and the module execute the simulation, either for a single pulse or for a sequence of pulses. The module includes sounds.

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[4] A spring of mass mo vibrates with a SHM of frequency fo .  Determine: (a) The elastic constant ko  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 Pi2)-1

Solution.-

Physics Virtual Lab (PVL):

Evolution of the energy in the Simple Harmonic Motion:

The PVL is a collection of -at least- 200 professional and highly interactive physics simulation modules, that can be used to learn and to teach physics.

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[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 coil-spring 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.