Oscillations of a mass on a spring.

[Death-Unit]

A mass m suspended from a spring of constant k has a period T. If a mass M is added, the period becomes 3T. Find M in terms of m.T=2pi(m/k)^(1/2)
I know that the period varies as the square root of the mass so the mass M should be 9 times that of m. The answer is M=8m. I don't know why it is 8 instead of 9. Any help would be appreciated.

Thanks

 

[hage567]

Your equation is a bit wrong (typo, maybe?), T=2pi(m/k)^(1/2). Have you worked it out mathematically? You will get M=8m. Remember that the total mass is M + m for when the period is 3T. Try to work it out.

 

[Death-Unit]

Nice. Inserting M+m then solving works. Thank you.