# Equation of Motion and other Physics Problems

6 What is the equation of motion for the idealized model shown?

7 For the idealized system shown, what is the natural circular frequency in rad/sec, and the period of oscillation in seconds?

1 The equivalent spring constant of two parallel springs with spring constants

20 lb/in., and 50 lb/in. is:

8 A Mass-Spring-Damper system is tested to determine the value of the viscous damping coefficient c. Assume k =150 N/m and m = 30 kg. The vibrational amplitude is observed to decrease to 33% of its initial value after two consecutive cycles. What is the value of the logarithmic decrement?

9 A Mass-Spring-Damper system is tested to determine the value of the viscous damping coefficient c. Assume k =150 N/m and m= 30 kg. The vibrational amplitude is observed to decrease 33% of its initial value after two consecutive cycles. What is the value of the viscous damping ratio?

10 A Mass-Spring-Damper system is tested to determine the value of the viscous damping coefficient c. Assume k= 150 N/m and m = 30 kg. The vibrational amplitude is observed to decrease to 33% of its initial value after two consecutive cycles. What is the value of the viscous damping coefficient c?

13 In the idealized model shown, m = 15 kg, k = 135 N/m, and the viscous damping ratio is 0.15. Assume that an external harmonic force F(t) = 15 cos 4 t acts on the system with F0=15 N and forcing frequency of 4 rad/s. Find the magnification factor M for the frequency ratio r of 1.382

See attached file for full problem description.

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#### Solution Preview

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6 What is the equation of motion for the idealized model shown?

7 For the idealized system shown, what is the natural circular frequency in rad/sec, and the period of oscillation in seconds?

1 The equivalent spring constant of two parallel springs with spring constants

20 lb/in., and 50 lb/in. is:

F = F1 + F2 = k1*x + k2*x = (k1 + k2)*x =kx => k =k1+k2 = 70 lb/in

8 A ...

#### Solution Summary

This solution describes how to determine the equation of motion and other physics problems.