A vertically oriented spring stretches 0.2m when a 0.4kg mass is suspended from it. The mass is pulled, stretching the spring by an additional 0.15m. The mass is released and beings to oscillate in SHM.

Question

a)Calculate the spring constant for the spring.
b)calculate the frequency of the oscillation.
c)calculate the total energy of the system.
d)calculate the magnitude of the velocity when the mass is 0.1m from the equilibrium position.
e)calculate the max acceleration of the oscillation

Answer 1

What is it that you are having difficultly with? This question is incredibly cookbook.

Answer 2

all of it.

Answer 3

you know force (mg) and stretch. Find k. F=kx

b. standard formula for period of a spring, period is 1/frequency.

c. total energy: 1/2 k (initial stretch)^2

d. 1/2 m v^2 + 1/2 k (.15)^2=totalenegy, solve for v.

e. acceleration=force/mass=kx/mass
where x is the max stretch given

Now the only thing left is the stretch to use in the formulas. The osclllation is caused by the additional stretch, use that.

Answer 4

well for the very first part;

Force = weight = m g
= 0.4 * 9.81 Newtons

displacement due to force = 0.2 meters

so

k = force/displacement
= 0.4*9.81/0.2 Newtons/meter

Now google simple harmonic motion mass spring