Question 3 A vehicle is modelled as a combined mass-spring-damper system that oscillates in the vertical direction only. The driver of the vehicle travels along a road whose elevation varies sinusoidally as shown in Figure 2. The mass of the vehicle, which includes the driver, is 2500 kg. The stiffness and damping of the shocks are 40 kN/m and 3000 kg/s respectively. i. Determine the amplitude of vibration of the vehicle when it travels at a constant speed of 90 km/hr along the sinusoidal road. ii. If additional load having a combined mass of 1000 kg is placed in the vehicle, determine the travelling speed of the vehicle that would result in a resonant condition. What is the amplitude of the vehicle at resonance? iii. Using an appropriate graph and suitable equations, explain how the oscillations of the vehicle can be significantly reduced when travelling at very high speeds. Please note that a simple graphical sketch with your pen that clearly identifies the key points is acceptable. Your axes must be also labelled correctly,
Question 3 A vehicle is modelled as a combined mass-spring-damper system that oscillates in the vertical direction only. The driver of the vehicle travels along a road whose elevation varies sinusoidally as shown in Figure 2. The mass of the vehicle, which includes the driver, is 2500 kg. The stiffness and damping of the shocks are 40 kN/m and 3000 kg/s respectively. i. Determine the amplitude of vibration of the vehicle when it travels at a constant speed of 90 km/hr along the sinusoidal road. ii. If additional load having a combined mass of 1000 kg is placed in the vehicle, determine the travelling speed of the vehicle that would result in a resonant condition. What is the amplitude of the vehicle at resonance? iii. Using an appropriate graph and suitable equations, explain how the oscillations of the vehicle can be significantly reduced when travelling at very high speeds. Please note that a simple graphical sketch with your pen that clearly identifies the key points is acceptable. Your axes must be also labelled correctly,
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Transcribed Image Text:Question 3
A vehicle is modelled as a combined mass-spring-damper system that oscillates in the vertical
direction only. The driver of the vehicle travels along a road whose elevation varies sinusoidally
as shown in Figure 2. The mass of the vechicle, which includes the driver, is 2500 kg. The stiffness
and damping of the shocks are 40 kN/m and 3000 kg/s respectively.
i. Determine the amplitude of vibration of the vehicle when it travels at a constant speed of
90 km/hr along the sinusoidal road.
ii. If additional load having a combined mass of 1000 kg is placed in the vehicle, determine
the travelling speed of the vehicle that would result in a resonant condition. What is the
amplitude of the vehicle at resonance?
Using an appropriate graph and suitable equations, explain how the oscillations of the
vehicle can be significantly reduced when travelling at very high speeds. Please note that
a simple graphical sketch with your pen that clearly identifies the key points is
acceptable. Your axes must be also labelled correctly.
iII.
Transcribed Image Text:y/m
-Velocity of vehicle
0.4
- Rigid massless tyre
0.2
20
distance (m)
-0.2
Figure 2
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