mass/springs question, please help :)

Question

What size mass would you put on a spring (k = 17.1 N/m) so it would oscillate with the same period as a 0.3 m long pendulum? (Use 9.81 m/s2 for g). 

 

in terms of kg.
to a precision of hundredths of a kg. Use a format like #.## in your answer. to an accuracy of 0.02 kg. 

 

thanks so much!

Answer 1

You want

 

√(k/m) = √(g/L)

 

k/m = g/L

 

m = kL/g = (17.1 N/m)(0.3 m) / (9.81 m/s²) ≅ 0.523 kg

Answer 2

You need to use 2 different equation for time period to come up with an answer

 

Here are the 2 equations:

 

1st equation --> T = 2π √(l/g)

T = time period

l = length of the pendulum

g = gravity

 

2nd equation --> T = 2π √(m/k)

 

First, we need to solve for the time period for 0.3 m long pendulum and we are going to use the first equation

 

T = 2π √(l/g)

T = 2π √(0.3/9.81)

T = 1.099 seconds

 

Now, rearranging the second equation to find the mass of the spring:

 

m = [(T^2)k]/(4π^2)

m = [(1.099^2)*17.1]/(4π^2)

m = 0.52 kg