A vertical mass-spring oscillator is displaced 2.0 cm from equilibrium. The 100 g mass passes through the equilibrium point with a speed of 0.75 m/s. What is the spring constant of the spring?
(A) 90 N/m
(B) 100 N/m
(C) 110 N/m
(D) 140 N/m
(E) 160 N/m

I was thinking of using kx = ma but then I realize that it is speed not a... :/ How do I do this problem?

Thank you.

Question

A vertical mass-spring oscillator is displaced 2.0 cm from equilibrium. The 100 g mass passes through the equilibrium point with a speed of 0.75 m/s. What is the spring constant of the spring?
(A) 90 N/m
(B) 100 N/m
(C) 110 N/m
(D) 140 N/m
(E) 160 N/m

I was thinking of using kx = ma but then I realize that it is speed not a... :/ How do I do this problem?

Thank you.

calculusfunctions · Answer

You're not there so I'll walk you through the mathematical steps!

Step 1:
Convert all units to fundamental units. i.e. grams to kilograms, and centimeters to meters.

Step 2:
Calculate the time, in seconds, it takes for the mass to reach the minimum position.

Step 3:
Divide the given speed by the time in step 2. This is your acceleration.

Step 4:
Find k

anonymous · Answer

try energy equation
$$\frac{ 1 }{ 2 }kx ^{2}=\frac{ 1 }{ 2 }mv ^{2}$$
using proper units