undamped spring-mass system with mass 6 kg and a spring which is stretched 2 meter by...

undamped spring-mass system with mass 6 kg and a spring which is stretched 2 meter by 10 Newtons. Suppose an oscillating force 3 cos(ωt) is acting on the system. What value of ω causes resonance? For this value of ω, find a formula for x, the distance between the weight and equilibrium t seconds after the weight starts at x = 0 at rest.

Solutions

Expert Solution

force by a streched string is

spring constant is

The equation of the spring with force acting on it is

its easy to handle if we use complex equation

and real part of the solution is required

In a steady state, the system oscillates as

inserting into equation

the value of omega that causes resonance is

the formule for x for this value of omega is

where

genius_generous answered 1 year ago

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