Simple harmonic motion problem

In summary, the maximum speed of the mass between 2 springs, oscillating between 2 points 5cm apart and completing 40 oscillations in 1 minute, is approximately 0.44 m/s. However, this answer may differ from the given answer of 0.44 m/s due to a possible error in the answer key.
  • #1
koat
40
0
A mass between 2 springs moves with shm.
it oscillates between 2 points 5cm apart and completes 40 oscillations in 1min
whats its max speed?

Please help i always get the wrong answer
The answer is 0.44 but why?
 
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  • #2
koat said:
A mass between 2 springs moves with shm.
it oscillates between 2 points 5cm apart and completes 40 oscillations in 1min
whats its max speed?

Please help i always get the wrong answer
The answer is 0.44 but why?

Show your solution attempt. We can't tell what's going wrong if we don't see what you're doing.
 
  • #3
2pi*40/60= 4/3 pi
f= 4/3pi*1/2= 2/3
vmax= 2pi*2/3*2.5*10^-2
but the answer is wrong :(
 
  • #4
koat said:
2pi*40/60= 4/3 pi
f= 4/3pi*1/2= 2/3
vmax= 2pi*2/3*2.5*10^-2
but the answer is wrong :(

Actually, your answer is correct. Looks like the answer key is wrong :smile:

You've correctly calculated the frequency of the oscillations:

## A = 5 cm/2 ##

## f = 40 cycles/min ##

##\omega = \frac{40 cycles}{min} \times \frac{1\;min}{60\;sec} \times \frac{2 \pi \; rad}{cycle} = \frac{4}{3}\pi \frac{rad}{sec}##

## v = A \omega = \frac{10 \pi}{3}\frac{cm}{sec} = 0.105 m/s ##
 
  • #5


I am unable to provide the answer to this specific problem without knowing the mass of the object and the spring constants of the two springs. However, I can provide some general information about simple harmonic motion and how to determine the maximum speed in this type of problem.

In simple harmonic motion, the object oscillates back and forth between two points at a constant frequency. The maximum speed occurs at the equilibrium point, where the object is at its furthest distance from the equilibrium position. This is because at this point, the forces from the two springs are at their maximum and the object experiences the maximum acceleration.

To calculate the maximum speed, you would need to use the equation v_max = Aω, where A is the amplitude (in this case, 5cm) and ω is the angular frequency (which can be calculated using the period, or 1min/40 oscillations in this case).

I cannot determine why the answer given is 0.44 without more information about the problem, but I suggest double checking your calculations and making sure all units are consistent. Additionally, it may be helpful to review the concept of simple harmonic motion and practice solving similar problems to gain a better understanding.
 

1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion where a system oscillates back and forth around a central equilibrium point. It can be described by a sinusoidal curve and is often seen in systems such as pendulums, springs, and mass-spring systems.

2. What is the equation for simple harmonic motion?

The equation for simple harmonic motion is x = A*sin(ωt + φ), where x is the displacement of the system from its equilibrium point, A is the amplitude of the motion, ω is the angular frequency, and φ is the phase angle.

3. How do I solve a simple harmonic motion problem?

To solve a simple harmonic motion problem, you will need to know the values of the amplitude, angular frequency, and phase angle. You can then use the equation x = A*sin(ωt + φ) to calculate the displacement of the system at a given time.

4. What is the relationship between period and frequency in simple harmonic motion?

The period of a simple harmonic motion is the time it takes for one complete oscillation, while the frequency is the number of oscillations per unit time. The two are inversely related, meaning that as the period increases, the frequency decreases and vice versa.

5. How does the mass affect the period of a simple harmonic motion?

In a simple harmonic motion, the mass does not affect the period of the motion. The period is only dependent on the stiffness of the system (represented by the angular frequency). This means that a system with a larger mass will have the same period as a system with a smaller mass, as long as their stiffnesses are equal.

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