Simple Harmonic Motion find Mass

However, there may be missing information or mistakes in the calculations that could affect the final answer.
  • #1
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Homework Statement


A block is attached to a horizontal spring with k = 75 N/m undergoes SHM with an amplitude of 0.15m. If the speed of the block is 1.7 m/s when the displacement is 0.12m from equilibrium, what is the mass of the block?

Homework Equations


E = E'
E[itex]_{k}[/itex] = [itex]\frac{1}{2}[/itex]mv[itex]^{2}[/itex]
E[itex]_{s}[/itex] = [itex]\frac{1}{2}[/itex]kx[itex]^{2}[/itex]

The Attempt at a Solution


E = E'
E[itex]_{k1}[/itex] + E[itex]_{s1}[/itex] = E[itex]_{s2}[/itex]
[itex]\frac{1}{2}[/itex]mv[itex]^{2}[/itex] + [itex]\frac{1}{2}[/itex]kx[itex]^{2}[/itex] = [itex]\frac{1}{2}[/itex]kx[itex]^{2}[/itex]
Where subscript 1 indicates that x = 0.12 m and subscript 2 indicates that x = 0.15 m (max energy)
Substituting in ...
m = 0.21 kg

but the answer is 0.27 kg?
 
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  • #2
With that data, the answer is m = 0.21 kg.
 

FAQ: Simple Harmonic Motion find Mass

How do you calculate the mass in a simple harmonic motion?

In simple harmonic motion, the mass can be calculated using the formula: mass = (force constant * amplitude) / (angular frequency)^2. The force constant and amplitude can be measured experimentally, while the angular frequency can be determined using the equation ω = 2πf, where f is the frequency of the motion.

Can the mass affect the period of a simple harmonic motion?

Yes, the period of a simple harmonic motion is directly proportional to the square root of the mass. This means that an increase in mass will result in a longer period and a decrease in mass will result in a shorter period.

How does the mass affect the amplitude of a simple harmonic motion?

The mass does not have a direct effect on the amplitude of a simple harmonic motion. However, a larger mass will require a larger force to maintain the motion, which may result in a smaller amplitude. On the other hand, a smaller mass will require a smaller force, allowing for a larger amplitude.

Is the mass the only factor that affects simple harmonic motion?

No, there are other factors that can affect simple harmonic motion, such as the force constant, amplitude, and damping force. These factors work together to determine the characteristics of the motion, including the period, amplitude, and frequency.

How can you determine the mass in a real-life example of simple harmonic motion?

In a real-life example, the mass can be determined by measuring the period and frequency of the motion and using the formula: mass = (force constant * amplitude) / (angular frequency)^2. The other variables can be measured or calculated using experimental data.

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