## Related questions with answers

Question

The motion of the outer frame B is given by $x_B = b sin \omega$t. For what range of the driving frequency $\omega$ is the amplitude of the motion of the mass m relative to the frame less than 2b?

Solutions

VerifiedSolution A

Solution B

Step 1

1 of 4Answered 10 months ago

Step 1

1 of 8**Given**

- The motion of the outer frame $x_{B}=b\sin{\omega t}$
- Amplitude $\abs{X}<2b$

**Analysis**

Set up the diagram of the dynamic forces. To find the relative amplitude of the mass, use the relative mass displacement $x=x_{abs}-x_{B}$, assume the $x_{abs}$ is constant. Find the differential equation of motion using the force diagram and solve it for $x=X\sin{\omega t}$. Extract the amplitude $X$ from the results of the differential equation and insert them into the given condition for the amplitude.

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