Are there enough information to solve these oscillation and wave problems?

In summary, the conversation is about two physics homework questions. The first question involves calculating the amplitude and phase difference of two oscillating springs with given values for spring constant and mass. The second question involves finding the potential energy and maximum acceleration of a harmonic oscillator with given values for spring constant and amplitude. The person asking for help has attempted to solve both questions but is unsure if there is enough information and is seeking clarification and assistance.
  • #1
ruppy99
1
0
Ok first time poster here so I hope I do this right. 2 assignment q's out of four I got I'm having trouble with. I think there might be missing info but I'm hoping for someone to back me up on this or to point me in the right direction.

Homework Statement


Q.1
Consider two identical ideal springs with a mass m attached which are harmonically
oscillating out of phase relative to each other, with the spring constant k = 100 Nm-1
and the mass m = 10-3 kg.
At the time t0 = + 0.1 sec the displacement of the spring 1 is x1(t0) = 10 mm and the
displacement of spring 2 is x1(t0) = 1 mm.
(i) Calculate the value of the amplitude A of each oscillation.
(ii) Calculate the value of the phase-difference φ between the two oscillators.

Q.2
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.

Homework Equations


Q.1
[tex]\omega[/tex]=[tex]\sqrt{k/m}[/tex]
f=[tex]\omega[/tex]/2pi
T=1/f
Q.2
1/2mv2+1/2kx2=total energy in harmonic oscillator

The Attempt at a Solution


Q.1
Found [tex]\omega[/tex]=316.23 rad/s, f=50.33hz and T=0.0199 yhen got stuck and wondered is there enough info..
Q.2
found total energy=0.005J, Kinetic energy at that point=0.004J and the x=1.41X10-3m
 
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  • #2
, but not sure how to calculate magnitude of the max acceleration. Any help would be appreciated. Thanks in advance.
 

1. What is an oscillation?

An oscillation is a repetitive back-and-forth movement or vibration around a central point or equilibrium. It is often described as a wave-like pattern.

2. What is the difference between an oscillation and a wave?

An oscillation refers to the repeated motion of an object, while a wave refers to the transfer of energy through a medium. An oscillation can create a wave, but a wave can also be created without an oscillation.

3. What is the relationship between frequency and wavelength in a wave?

Frequency and wavelength are inversely proportional in a wave. This means that as the frequency increases, the wavelength decreases, and vice versa. This relationship is described by the equation: wavelength = speed of wave / frequency.

4. How are sound waves and light waves similar and different?

Both sound waves and light waves are forms of energy that travel in a wave-like pattern. However, sound waves require a medium (such as air or water) to travel through, while light waves can travel through a vacuum. Additionally, sound waves are longitudinal waves, while light waves are transverse waves.

5. What are some real-world applications of oscillations and waves?

Oscillations and waves have a wide range of practical applications, including in communication technologies such as radios and cell phones, medical imaging techniques such as ultrasound and MRI, and musical instruments. They are also used in seismology for studying earthquakes and in weather forecasting for analyzing atmospheric waves.

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