The formula for a simple harmonic oscillator is x(t) = Acos (ωt + φ) 1. A block of mass 4.3 kg is dropped from 3.6 m above the ground onto an initially unstretched massless spring of spring constant 26 k/Nm^-1 and equilibrium length 0.40m. How long does it take until the block comes into contact with the spring? Recall that there is gravity of g = 9.8 ms^−2. 2. Neglecting any disspative effects, how far does the spring compress from its unstretched position when the block falls on it ? Recall that the reis gravity of g = 9.8ms^−2. 3. How long does it take from the moment the block contacts the spring until the spring is maximally compressed ? 4. Describe in words what would happen after the spring reaches its maximal compression. Does the motion sound realistic? What real-world effects are important to include in order to describe a realistic situation ?
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.
The formula for a simple harmonic oscillator is x(t) = Acos (ωt + φ)
1. A block of mass 4.3 kg is dropped from 3.6 m above the ground onto an initially unstretched massless spring of spring constant 26 k/Nm^-1 and equilibrium length 0.40m. How long does it take until the block comes into contact with the spring? Recall that there is gravity of g = 9.8 ms^−2.
2. Neglecting any disspative effects, how far does the spring compress from its unstretched position when the block falls on it ? Recall that the reis gravity of g = 9.8ms^−2.
3. How long does it take from the moment the block contacts the spring until the spring is maximally compressed ?
4. Describe in words what would happen after the spring reaches its maximal compression. Does the motion sound realistic? What real-world effects are important to include in order to describe a realistic situation ?
Step by step
Solved in 2 steps
