How Is Maximum Acceleration Calculated in a Harmonic Oscillator?

In summary, waves and oscillations are physical phenomena that involve the periodic motion of a medium or a system around an equilibrium point. There are several types of waves, including mechanical waves, electromagnetic waves, and matter waves. Waves and oscillations are closely related, with oscillations creating waves that can be described by their frequency, amplitude, and wavelength. Transverse and longitudinal waves differ in the direction of particle movement. Waves and oscillations have practical applications in communication, medical imaging, music, and mechanical systems.
  • #1
loyol2degame
1
0
I need help with this question.

The potential energy stored in a harmonic oscillator at time t0 = -0.5 s is 1 mJ. The
spring-constant associated with the oscillator has the value k = 103 N m-1 and the
oscillation amplitude is A = 10-6 m.

Calculate the magnitude of the maximum acceleration.
 
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  • #2
Is that k = 103 Nm-1 or k = 103 nm-1 ?

Actually, neither make much sense with an amplitude of only 10-6m and given the figure for energy stored. The maximum stored potential energy should be

[tex] PE_{max} = \frac{1}{2}k A^2 [/tex]

which is about 5 x 10-10 Joules if k = 103 N/m.
 
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Related to How Is Maximum Acceleration Calculated in a Harmonic Oscillator?

1. What are waves and oscillations?

Waves and oscillations are physical phenomena that involve the periodic motion of a medium or a system around an equilibrium point. They can be described as the transfer of energy from one point to another without the transfer of matter.

2. What are the different types of waves?

There are several types of waves, including mechanical waves, electromagnetic waves, and matter waves. Mechanical waves, such as sound waves, require a medium to propagate. Electromagnetic waves, such as light waves, can travel through a vacuum. Matter waves are associated with the motion of particles, such as electrons.

3. How are waves and oscillations related?

Waves and oscillations are closely related because oscillations are the repeating motion that creates waves. Oscillations can be simple, such as the back and forth motion of a pendulum, or complex, such as the vibrations of a guitar string. These oscillations create waves that can be described by their frequency, amplitude, and wavelength.

4. What is the difference between transverse and longitudinal waves?

Transverse waves are waves in which the particles of the medium move perpendicular to the direction of wave propagation. Examples include water waves and electromagnetic waves. Longitudinal waves are waves in which the particles of the medium move parallel to the direction of wave propagation. Examples include sound waves and seismic waves.

5. How are waves and oscillations used in everyday life?

Waves and oscillations have many practical applications in everyday life. They are used in communication systems, such as radio and television, and in medical imaging technologies such as ultrasound. They also play a crucial role in music and sound production, and in the functioning of many mechanical systems, such as engines and motors.

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