A 0.23 kg mass is suspended on a spring which stretches a distance of 5.3 cm. The mass is then pulled down an additional distance of 11 cm and released. What is the displacement from the equilibrium position with the mass attached (in cm) after 0.33 s? Take up to be positive and use g = 9.81 m/s2. The initial condition should be set as y(0)=-A because the mass is pulled below the equilibrium (the origin along y-axis) and released. Hint: Get k from the displacement as it was done in this example. The equation will have ω = (k/m)1/2, and the phase will be such that it will be a cosine with a negative amplitude, because it starts at a negative displacement.
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 0.23 kg mass is suspended on a spring which stretches a distance of 5.3 cm. The mass is then pulled down an additional distance of 11 cm and released. What is the displacement from the equilibrium position with the mass attached (in cm) after 0.33 s? Take up to be positive and use g = 9.81 m/s2. The initial condition should be set as y(0)=-A because the mass is pulled below the equilibrium (the origin along y-axis) and released. Hint: Get k from the displacement as it was done in this example. The equation will have ω = (k/m)1/2, and the phase will be such that it will be a cosine with a negative amplitude, because it starts at a negative displacement. |
Step by step
Solved in 4 steps with 4 images
