A block of mass 0.15 kg in the horizontal plane is attached to the end of a spring with force constant k = 0.90 N / m. A damping force proportional to speed acts on the system due to friction. The damping constant is b = 0.20 kg / s. A harmonic external force given by F (t) = F0 cost is imposed on this system. Here F0 = 3 N. a) Calculate the resonance frequency (R) b) Calculate the steady-state amplitude in the resonance state.
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
A block of mass 0.15 kg in the horizontal plane is attached to the end of a spring with force constant k = 0.90 N / m. A damping force proportional to speed acts on the system due to friction. The damping constant is b = 0.20 kg / s. A harmonic external force given by F (t) = F0 cost is imposed on this system. Here F0 = 3 N.
a) Calculate the resonance frequency (R)
b) Calculate the steady-state amplitude in the resonance state.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 4 images
