Calculating SHM Parameters: Speed and Acceleration at Different Points

In summary, a 2kg body with a force constant of 3.16N/m undergoes simple harmonic motion with an amplitude of 30mm. The acceleration at the midpoint is 0 and the velocity at the end of the path is 0. To find the speed and acceleration at a point 20mm from the midpoint, you can use basic equations for SHM and solve for omega in terms of mass and force constant.
  • #1
KingBigness
96
0
A 2kg body, moving under the influence of a force constant of 3.16N/m, vibrates in SHM with an amplitude of 30mm. Determine the speed and the acceleration,
a) at the midpoint of the vibration (ie. zero displacement)
b) at the end of the path (ie. Max displacement)
c) at a point 20mm from the midpoint


I know that for a) the acceleration will be 0 and for b) the velocity will be 0...but I am not sure how to work out the rest of it...i have many equations that will give me the answer but i need to know omega..which i can not work out.

any help would be greatly appreciated

Thank you!
 
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  • #2
KingBigness said:
i have many equations that will give me the answer but i need to know omega..which i can not work out.
One of the most basic equations describing SHM tells you how to find omega in terms of m and k. (Look it up!)
 
  • #3
Doc Al said:
One of the most basic equations describing SHM tells you how to find omega in terms of m and k. (Look it up!)

omg I'm a complete spastic...i didn't even register that 'constant force' is k (force constant)

wow i feel completely stupid now.

sorry for wasting your time!
 

Related to Calculating SHM Parameters: Speed and Acceleration at Different Points

1. What is Simple Harmonic Motion?

Simple Harmonic Motion (SHM) is a type of periodic motion where a system oscillates back and forth around an equilibrium position due to a restoring force that is directly proportional to the displacement from the equilibrium position.

2. What are the characteristics of Simple Harmonic Motion?

The characteristics of SHM include a constant amplitude, a constant period (time for one complete oscillation), and a sinusoidal displacement-time graph. The system also experiences maximum velocity at the equilibrium position and maximum acceleration at the maximum displacement.

3. What is the formula for Simple Harmonic Motion?

The formula for SHM is x = A sin(ωt + φ), where x is the displacement from the equilibrium position, A is the amplitude, ω is the angular frequency, t is time, and φ is the phase angle. This formula can also be written in terms of velocity and acceleration, v = Aω cos(ωt + φ) and a = -Aω² sin(ωt + φ).

4. What are some real-life examples of Simple Harmonic Motion?

Some examples of SHM include a swinging pendulum, a mass on a spring, and a vibrating guitar string. SHM can also be observed in the motion of objects attached to a rotating wheel or in the motion of a car's suspension system.

5. How is Simple Harmonic Motion related to energy?

In SHM, the total mechanical energy of the system (potential energy + kinetic energy) remains constant as the system oscillates. At the equilibrium position, the energy is all in the form of potential energy, and at the maximum displacement, the energy is all in the form of kinetic energy. This relationship is described by the conservation of energy principle.

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