What Are the Characteristics of Oscillations for a Box on a Spring?

In summary, the position of the center of the box is given by the equation x = 5.3 m * cos(20/sec * t). After 2 seconds, the position is 4.98 m. The amplitude of the box's oscillations is 5.3 m and the period is 0.05 seconds. The maximum velocity is 5.3 m/s and the maximum acceleration is 106 m/s^2. It takes the box 0.1 seconds to move from -2.65 m to +2.65 m. A = 5.3 m and ω = 20 s^-1.
  • #1
mattmannmf
172
0
the position of the center of the box shown is given by the equation

x = 5.3 m * cos(20/sec * t)
(a) What is the position of the box 2 seconds after the oscillations have started?

(b) What is the amplitude of the box's oscillations?

(c) What is the period of the box's oscillations?

(d) What is the box's maximum velocity?

(e) What is the box's maximum acceleration?

(f) How long does it take the box to move from -2.65 m to +2.65 m?

for a, i just plugged in 2 for t and got 4.98...but that's wrong not sure where to go from there
Calc:
5.3*cos(20/(1/cos(2)))...sec= 1/cos
 
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  • #2


Start with x = A cos (ωt). What is A? What is ω?

A = 5.3 m, and ω = 20 s-1
 
  • #3


so x=5.3*cos(20E-1*2)...5.28?
 

1. What is an oscillation?

An oscillation is a repetitive movement or fluctuation around a central point or equilibrium. It can be seen in various natural phenomena such as the movement of a pendulum or the vibration of a guitar string.

2. How does frequency affect oscillations?

The frequency of an oscillation refers to the number of cycles or repetitions of the movement per unit of time. It is directly related to the energy and amplitude of the oscillation, with higher frequencies having more energy and larger amplitudes. This means that the higher the frequency, the faster and more intense the oscillations will be.

3. What factors affect the period of an oscillation?

The period of an oscillation is the time it takes for one complete cycle of the movement. It is affected by the length of the oscillating object, the mass of the object, and the strength of the restoring force (such as gravity or tension). A longer length, larger mass, and stronger restoring force will result in a longer period.

4. How do damping and resonance impact oscillations?

Damping refers to the gradual decrease in amplitude of an oscillation over time due to the dissipation of energy. This can be caused by external factors such as friction or air resistance. On the other hand, resonance occurs when an oscillating system is driven at its natural frequency, resulting in a buildup of energy and a larger amplitude of oscillation. Both damping and resonance can significantly affect the behavior and stability of oscillating systems.

5. What are some real-world applications of oscillations?

Oscillations have numerous practical applications in fields such as engineering, medicine, and technology. Some examples include the use of pendulums in clocks, the vibration of guitar strings to produce music, and the oscillation of electrons in electronic devices to generate radio waves. In medicine, oscillations are used in devices such as pacemakers and ultrasound machines. They also play a crucial role in the study of earthquakes and seismology.

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