Simple Harmonic Motion, platform and box

In summary, the conversation discusses the calculation of the shortest period of motion for a platform in simple harmonic motion, with amplitude 0.035 m, so that a block of wood remains in constant contact with it. The equation for maximum acceleration is given and used to solve for the angular frequency and frequency, resulting in a period of 0.0224 seconds. However, the formula for maximum acceleration is incorrect, leading to an incorrect solution.
  • #1
sheepcountme
80
1

Homework Statement



A platform moves up and down in SHM, with amplitude 0.035 m. Resting on top of the platform is a block of wood. What is the shortest period of motion for the platform so that the block will remain in constant contact with it?


Homework Equations



a(t)=-A[tex]\omega[/tex]^2cos([tex]\omega[/tex]t+phase constant)
amax=A[tex]\omega[/tex]

The Attempt at a Solution



I didn't see how I could possibly use the first one with so many unknowns so I used amax=A[tex]\omega[/tex] and set amax=9.8 figuring that the amount couldn't be more than gravity otherwise the block and platform would separate (maybe I'm wrong in this).
And so I set 9.8=.035[tex]\omega[/tex] and solved (getting 280). The I used [tex]\omega[/tex]=2[tex]\pi[/tex]f and solving for f (getting 140/[tex]\pi[/tex]) and then using f=1/T and solved for T getting .0224 which was incorrect.
 
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  • #2
Check your formula for amax, it is not correct.

ehild
 
  • #3
Oh, it came out funny. It's supposed to be amax=A x omega. Is this still incorrect? If it is, I really need to throw a fit about a refund.
 
  • #4
No, see the previous line. a must be m/s2, yours is m/s.

ehild
 

Related to Simple Harmonic Motion, platform and box

1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object oscillates back and forth around an equilibrium point, following a path that is symmetric about the equilibrium point. The force acting on the object is directly proportional to its displacement from the equilibrium point and is directed towards the equilibrium point.

2. How is simple harmonic motion related to a platform and box?

The platform and box system is often used as a physical representation of simple harmonic motion. The platform acts as the equilibrium point, while the box represents the object undergoing periodic motion. The force acting on the box is provided by a spring attached to the platform, which causes the box to oscillate back and forth.

3. What factors affect the frequency of simple harmonic motion?

The frequency of simple harmonic motion is affected by the mass of the object, the stiffness of the spring, and the amplitude of the oscillations. Increasing the mass or stiffness will decrease the frequency, while increasing the amplitude will increase the frequency.

4. How does simple harmonic motion differ from other types of periodic motion?

Simple harmonic motion is different from other types of periodic motion in that it follows a specific mathematical pattern known as a sine wave. Other types of periodic motion, such as circular motion, do not follow this pattern and have different equations governing their behavior.

5. What are some real-life examples of simple harmonic motion?

Simple harmonic motion can be observed in many systems in nature and in daily life. Some common examples include the motion of a pendulum, the vibrations of a guitar string, and the motion of a mass attached to a spring. It is also seen in tidal waves, sound waves, and the motion of celestial bodies such as planets and stars.

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