Vibration Analysis Questions -
Q1. Use the energy method to determine the equations of motion and the natural frequency for the given system. Assume there is no slippage between the pulley and the cord.
![2176_fig1.png](https://secure.tutorsglobe.com/CMSImages/2176_fig1.png)
Q2. A helicopter blade and rotor assembly is shown in Fig. Make the necessary assumptions to simplify the problem and deduce the equation of motion for the flapping motion of the blade.
![1961_fig2.png](https://secure.tutorsglobe.com/CMSImages/1961_fig2.png)
Q3. The left end of the cantilever beam shown in Fig. undergoes the harmonic motion x(t)=A cos(wt). Derive the differential equation for the motion of the mass M and determine the resonance frequency. Assume that the beam is massless and that its bending stiffness EI is constant.
![347_fig3.png](https://secure.tutorsglobe.com/CMSImages/347_fig3.png)
Q4. The support of the viscously damped pendulum shown in Fig. undergoes harmonic oscillation. Derive the differential equation of motion of the system, then assume small amplitudes and solve for θ (t).
![317_fig4.png](https://secure.tutorsglobe.com/CMSImages/317_fig4.png)
Q5. For the system shown in Fig., set up the equations of motion and solve for the steady state amplitude and phase angle by the use of complex algebra.
![1546_fig5.png](https://secure.tutorsglobe.com/CMSImages/1546_fig5.png)
Q6. Fig. represents a simplified diagram of a spring supported vehicle travelling over a rough road. Determine the equation for the amplitude of W as a function of the speed and determine the most unfavorable speed.
![852_fig6.png](https://secure.tutorsglobe.com/CMSImages/852_fig6.png)
Q7. An undamped vibration pickup having a natural frequency of 1 cps is used to measure a harmonic vibration of 4 cps. If the amplitude indicated by the pickup (relative amplitude between pickup mass and frame) is 0.052cm, what is the correct amplitude?
Q8. An aircraft radio weighing 106.75 N is to be isolated from engine vibrations ranging from 1600 to 2200 cpm. What statical deflection must the isolators have for 85 per cent isolation?