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Newton's second law and SHM

  • #1
rock.freak667
Homework Helper
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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

keq=2k

ω=√keq/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
 

Answers and Replies

  • #2
1,860
0
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. :)
 
Last edited:

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