Finding Spring Stiffness and Effective Mass for Suspended Beam

[rock.freak667]

Homework Statement

A cable is used to suspend a 400 kg safe. It is being lowered at 6 m/s, when it stops suddenly. Find the maximum dynamic tension and the frequency of vibration. k=2(10⁵ N/m

Homework Equations

Newton's 2nd law

The Attempt at a Solution

Well I easily found the frequency using ω=k/m and got the correct answer.

If I find the resultant force in the direction of mg, I get mg-T=ma. I am not given a, I am given, v.

Homework Statement

A uniform beam is suspended by 2 springs A & B. Unloaded, the period of vertical vibration is 0.83s. When 50kg is loaded onto its centre, the period is 1.52s. Find the spring stiffness of each spring and the effective mass of the beam

Homework Equations

The Attempt at a Solution

The springs would be in parallel so

k_eq=2k

ω=√k_eq/m ⇒(2π/0.83)^2 (50) = 2k, but this does not give me the correct answer. k=608 N/m. I get 1432.66 N/m

 

[Mindscrape]

1) Right, the velocity they give you will be an initial condition that you can use with the general equation for a mass on a spring. Max tension should be at max deceleration.

2) It gives you the period for the unloaded beam. Once the beam is loaded with more mass it will have a different period. :)