Evergy of Simple harmonic motion

[Jake4]

Homework Statement

A 0.155 kg mass is attached to a spring and
executes simple harmonic motion with a pe-
riod of 0.63 s. The total energy of the system
is 1.9 J.
Find the force constant of the spring.

Homework Equations

E=1/2(kA^2)

The Attempt at a Solution

We went over in class, how to find the spring constants and such when given the amplitude. However I can't figure out how to work this one out. I think I'm missing a piece. I'm assuming there's a way to find A from the period?

any help would be wonderful, thank you guys!

 

[lepton5]

do you know the relation between [tex]\omega[/tex], k and m ?

 

[Jake4]

I do not.. >.<

 

[suwarna07]

Homework Statement

A 0.155 kg mass is attached to a spring and
executes simple harmonic motion with a pe-
riod of 0.63 s. The total energy of the system
is 1.9 J.
Find the force constant of the spring.

Homework Equations

E=1/2(kA^2)

The Attempt at a Solution

We went over in class, how to find the spring constants and such when given the amplitude. However I can't figure out how to work this one out. I think I'm missing a piece. I'm assuming there's a way to find A from the period?

any help would be wonderful, thank you guys!

we know that w = 2 pi / T
w = 9.97

and we also know,

w squared = k/m

hence solving for k you get k = 1.54 N/m

 

[rwisz]

I can provide a response to this content by explaining the concept of energy in simple harmonic motion and how to calculate the force constant of a spring in this scenario. In simple harmonic motion, the total energy of the system is the sum of the kinetic energy (KE) and potential energy (PE). This can be represented by the equation E = 1/2kA^2, where k is the force constant of the spring and A is the amplitude of the motion.

In this scenario, we are given the period of the motion (0.63 s) and the total energy of the system (1.9 J). To find the force constant, we need to find the amplitude of the motion. This can be done by using the equation T = 2π√(m/k), where T is the period, m is the mass of the object, and k is the force constant. Rearranging this equation, we get A = √(2E/mω^2), where ω is the angular frequency (2π/T).

Substituting the given values into this equation, we get A = √(2*1.9/0.155*(2π/0.63)^2) = 0.18 m. Now, we can use this value of A in the equation E = 1/2kA^2 to solve for k. This gives us k = 2E/A^2 = 2*1.9/(0.18)^2 = 58.02 N/m.

Therefore, the force constant of the spring in this scenario is 58.02 N/m. This value can be used to determine the restoring force of the spring at any point in the motion and can also be used to predict the behavior of the system in other situations.