A frictionless mass/spring system is as shown in Figure Q3. The spring stiffness, k, and mass,...

 

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A frictionless mass/spring system is as shown in Figure Q3. The spring stiffness, k, and mass, m, are 1000 N/m and 25 kg respectively. When time t = 0 secs the mass is displaced by 10 cm and released from rest. For the system : a) Determine the natural frequency of the resulting vibration, b) Calculate the strain energy stored in the spring before the mass is released, [5 marks] c) Determine the equation of motion relating the displacement, x, and time, t, and sketch on a suitable graph, [10 marks] d) State the position of the maximum velocity and acceleration of the mass on the sketch given in part c). [6 marks] k 3 X [4 marks] Figure Q3 Mass/spring Vibration System A frictionless mass/spring system is as shown in Figure Q3. The spring stiffness, k, and mass, m, are 1000 N/m and 25 kg respectively. When time t = 0 secs the mass is displaced by 10 cm and released from rest. For the system : a) Determine the natural frequency of the resulting vibration, b) Calculate the strain energy stored in the spring before the mass is released, [5 marks] c) Determine the equation of motion relating the displacement, x, and time, t, and sketch on a suitable graph, [10 marks] d) State the position of the maximum velocity and acceleration of the mass on the sketch given in part c). [6 marks] k 3 X [4 marks] Figure Q3 Mass/spring Vibration System

Answer rating: 100% (QA)

SOLUTION a The natural frequency of the massspring system can be calculated using the formula km where k is the spring stiffness and m is the mass Given that k 1000 Nm and m 25 kg we can substitute th... View the full answer