Calculate Particle's Speed in SHM with Period of 2.4 s and Amplitude of .1 m

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In summary, for a particle vibrating in SHM with a period of 2.4 s and an amplitude of .1 m, it takes 0.4 s to move from one end of its path to a point .05 m from the equilibrium position. The particle's speed at this position is approximately .227 m/s.
  • #1
timtng
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A particle vibrates in SHM with the period of 2.4 s and the amplitude of .1 m.

a) How long is required for the particle to move from one end of its path to the nearest point .05 m from the equilibrium position?
b) What is the particle's speed at this position?

for a) this is what I did
x=Acos(ωt), 5=10cos(ωt), ω=2pi/T=2pi/2.4=2.62
t=arccos(.5)/2.62= 0.4 s

I'm a little confused on part b.

Please see if I did a correctly, and show me how to answer b.

Thanks
 
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  • #2
Part (a) looks fine. For part (b), you have to take the time derivative of position to get the velocity,

v = dx/dt = -Aω sin(ωt)
 
  • #3
so v=-(.1)(2.62)(sin(2.62*.4))= .00479 m/s

Is that correct?
 
  • #4
Originally posted by timtng
so v=-(.1)(2.62)(sin(2.62*.4))= .00479 m/s

Is that correct?

Almost; you have to switch your calculator to radians to take the sine.
 
  • #5
Okay, so it should be .227 m/s?
 
  • #6
Yes.
 

1. What is SHM and how does it relate to calculating particle speed?

SHM stands for Simple Harmonic Motion, which is a type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position. In order to calculate the particle's speed in SHM, we need to use the formula v = 2πA/T, where A is the amplitude and T is the period.

2. How do I determine the period and amplitude in SHM?

The period, denoted as T, is the time it takes for one complete cycle of motion in SHM. It can be calculated by using the formula T = 2π√(m/k), where m is the mass of the particle and k is the spring constant. The amplitude, denoted as A, is the maximum displacement from the equilibrium position and can be measured directly from the motion of the particle.

3. Can I use the same formula for calculating particle speed in all types of SHM?

Yes, the formula v = 2πA/T can be used for calculating particle speed in all types of SHM, as long as the period and amplitude are known.

4. What are the units for particle speed in SHM?

The units for particle speed in SHM are meters per second (m/s). This is because the amplitude (A) and period (T) are both measured in meters and seconds respectively, and when divided, the units cancel out, leaving only meters per second.

5. Can I use this formula to calculate the speed of a particle in circular motion?

No, this formula is specifically for calculating particle speed in SHM. For circular motion, a different formula is used, which takes into account the radius of the circular path and the angular velocity of the particle.

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