Finding the Mass Required for Double the Velocity in a Spring-Mass System

In summary, the conversation discusses the calculation of the mass required to produce double the maximum velocity for a suspended mass of 0.3kg using a spring with a stiffness of 200Nm. The resulting calculation suggests a mass of 0.07kg, but there is a discrepancy with the laws of physics. The discrepancy is due to the assumption that a higher mass should result in a higher velocity, when in reality, the acceleration is affected by the mass and not the velocity.
  • #1
brenfox
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1

Homework Statement


A mass of 0.3kg is suspended from a spring of stiffness 200Nm. If the mass is displaced by 10mm from its equilibrium position and released for the resulting vibration, calculate:
The mass required to produce double the maximum velocity calculated in question 2 using the same spring and deflection. The velocity in question 2 being 0.26ms-1.


Homework Equations


V=Aωcos(ωt+∅)
ω=√k/m

The Attempt at a Solution


So A=0.01 v= 0.52MS-1.
So transposing ωcos = 0.52/0.01 = 52rads.

Now with these numbers i can find the mass.
ω=√k/m
Transposing m = k/m^2
Mass = 0.07kg.

Now the laws of physics are telling me this answer cannot be right. If an object with a mass of 0.3kg possesses a velocity of 0.26ms-1, then an object with a velocity of 0.52ms-1 should be greater than 0.07kg. The velocity is higher so surely the mass must be greater. Where am i going wrong with this!. Any help would be appreciated.
 
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  • #2
I see no reason why a greater mass should mean a higher velocity. Think about the acceleration. A higher mass has greater inertia, but the same deflection of the same spring only produces the same force.
Maybe you are subconsciously taking the greater mass case also to have a greater displacement as part of a general scaling up. In that case you could get a greater velocity.
 
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1. What is spring velocity?

Spring velocity is the speed at which an object attached to a spring moves back and forth when the spring is stretched or compressed.

2. How is spring velocity calculated?

Spring velocity can be calculated using the equation v = √(k/m), where v is the velocity, k is the spring constant, and m is the mass of the object attached to the spring.

3. What factors affect spring velocity?

The factors that affect spring velocity include the spring constant, the mass of the object attached to the spring, and the amplitude of the spring's oscillations.

4. Can spring velocity be negative?

Yes, spring velocity can be negative if the object attached to the spring is moving in the opposite direction of the original displacement.

5. How does changing the spring's stiffness affect its velocity?

Increasing the spring's stiffness (spring constant) will result in a higher spring velocity, while decreasing the stiffness will result in a lower spring velocity.

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