What Is the Maximum Speed in This Simple Harmonic Motion Problem?

[koat]

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?

 

[gneill]

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.

 

[koat]

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 :(

 

[gneill]

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

You've correctly calculated the frequency of the oscillations:

$A = 5 cm/2$

$f = 40 cycles/min$

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

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

 

[asteriatic]

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.