Solving SHM Spring Mass Homework Problem

Once you have k, you can use the formula for T to find the period. To find the mass, use the formula kx=mg where x is the additional displacement of 8.74 cm and the force is given as 88.7 N. Solving for m, you should get a positive value. Finally, to find the energy, use the formula E= 1/2kA2 where A is the amplitude, which is equal to the maximum deformation of the spring. In summary, you can find the period of oscillation by using the formula T=2pi(m/k)^.5, the mass by using the formula kx=mg, and the energy by using the formula E= 1/2
  • #1
laxbrah44
1
0

Homework Statement



A spring of unstretched length L0 = 60.5 cm and spring constant K is suspended vertically as shown. A mass m is attached to the spring and it stretches the spring to a length of 123 cm. Then the mass is pulled down an additional 8.74 cm from the equilibrium position and released. At its maximum deformation, the spring force is 88.7 N.

A. What is the period of the oscillation?
B. What is the mass m?
C. What is the spring constant K?
D. What is the energy in the oscillation?

Homework Equations



kx=mg T=2pi(m/k)^.5 E= 1/2kA2


The Attempt at a Solution



I found the period as 1.58s by doing (stretched - unstretched) / 9.8 and then sq root that then multiply by 2pi. However, I am completely lost on how to find mass. Using substitution, etc always gets me a negative number. Once I know how to get mass it'll be easy to find K and Energy. Thanks
 
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  • #2
You want to find k first. Use the info you were given in the last sentence.
 

Related to Solving SHM Spring Mass Homework Problem

1. How do I find the period of a spring mass system?

The period of a spring mass system can be found using the formula T = 2π√(m/k), where T is the period, m is the mass of the object attached to the spring, and k is the spring constant.

2. What is the difference between simple harmonic motion and damped harmonic motion?

Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement and acts in the opposite direction of the displacement. Damped harmonic motion is when there is an additional force acting on the system that causes the amplitude of the motion to decrease over time.

3. How do I calculate the amplitude of a spring mass system?

The amplitude of a spring mass system can be calculated by measuring the maximum displacement from equilibrium. It can also be found by dividing the maximum energy of the system by the spring constant.

4. What is the relationship between the spring constant and the frequency of a spring mass system?

The frequency of a spring mass system is inversely proportional to the square root of the spring constant. This means that as the spring constant increases, the frequency of the system decreases.

5. How do I determine the velocity and acceleration of a spring mass system?

The velocity and acceleration of a spring mass system can be found by taking the derivative of the displacement equation. Velocity is the first derivative and acceleration is the second derivative of displacement with respect to time.

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