An object spring system moving with simple harmonic motion has an amplitude A.
a) What is the total energy of the system in terms of k and A only? (E=1/2kA^2)
b) Suppose at a certain instant the kinetic energy is twice the elastic potential energy. Write an equation describing this situation, using only the variables for the mass m, velocity v, spring constant k, and position x. (1/2mv^2=kx^2)
c) Using the results of parts (a) and (b) and the conservation of energy equation, find the positions x of the object when its kinetic energy equals twice the potential energy stored in the spring.
Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
the total energy is kA^2/2=P.E+k.E=3P.E
This gives P.E=kA^2/6=kx^2/2
Solve it for x
I need part C. I'm not sure how to exactly get it but the answer is: x=A/3^1/2
If you can expand your steps a bit, I would appreciate it.
Not the answer you are looking for? Search for more explanations.
the total energy is conserved in SHM and is equal to kA^2/2 at all the times.
The total energy is the sum of the potential energy and the kinetic energy.
Given K.E.=2P.E. at some instant and we have to find the value of x at which thia will happen
This can be solved for x and x is indeed equal to A/3^1/2