The damped oscillation equation is usually described by the expression (in the image) b -damping constant Regarding damped oscillations and considering the text above, evaluate the following information. I) Considering that α = ω0, the expression x=(A + B t)e^-(α t) is a solution of the differential equation of the damped oscillation. II) Considering that at the instant of time t=0, the position is x=x0 and the velocity v=0, then the acceleration of the damped oscillatory system for t=0 is given by a=-(ω0)²x0 III) Considering that at a certain instant of time, the position is x and the acceleration is a, then the velocity is given by (image 2) Choose an option: a)I and III, only. b)I and II, only. c)II and III, only. d)I, only. e)I, II and III.
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 damped oscillation equation is usually described by the expression (in the image)
b -damping constant
Regarding damped oscillations and considering the text above, evaluate the following information.
I) Considering that α = ω0, the expression x=(A + B t)e^-(α t) is a solution of the differential equation of the damped oscillation.
II) Considering that at the instant of time t=0, the position is x=x0 and the velocity v=0, then the acceleration of the damped oscillatory system for t=0 is given by a=-(ω0)²x0
III) Considering that at a certain instant of time, the position is x and the acceleration is a, then the velocity is given by (image 2)
Choose an option:
a)I and III, only.
b)I and II, only.
c)II and III, only.
d)I, only.
e)I, II and III.
Step by step
Solved in 5 steps
