1 / 10

Oscillatory Motion

Oscillatory Motion. SHM – Simple Harmonic Motion Spring Systems Pendulums. Oscillatory Motion. Any motion that is a repetitive back and forth motion is considered oscillatory motion. Periodic Motion Harmonic Motion Vibration

clarke-miranda
Télécharger la présentation

Oscillatory Motion

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Oscillatory Motion SHM – Simple Harmonic Motion Spring Systems Pendulums

  2. Oscillatory Motion Any motion that is a repetitive back and forth motion is considered oscillatory motion. Periodic Motion Harmonic Motion Vibration This type of motion involves an object that moves about some equilibrium position. The displacement of the object is proportional to the force acting on it. The force is always directed towards the equilibrium position.

  3. SHM The position of an object undergoing SHM over a period of time follows the function: A is the amplitude, the maximum displacement of the object ω is the angular frequency ϕ is the phase constant or phase angle and is determined by the initial displacement and velocity of the particle The quantity (ωt+ ϕ) is called the phase of the motion and is helpful when you are comparing the motions of two oscillators An x -vs.-tgraph for an object undergoing SHM. The bottom graph depicts the special case in which x = A at t = 0 and henceϕ = 0

  4. Period A vibrating system that oscillates in periodic motion is said to be undergoing simple harmonic motion. A single sequence of this motion is known as a cycle. The time it takes for the completion of one full cycle is known as a period (T). For example, the period of one Earth rotation is approximately 24 hours. ωT = 2π (the angular velocity x the time for a full cycle gives one full cycle, 2π) Therefore the period can be given by: T = 2π/ω

  5. Frequency The inverse of the period is the frequency, f. The frequency is the number of oscillations that the particle makes per unit of time: The unit for frequency is Hz, which is s-1 Which means we can get other expressions for the angular velocity of angular frequency:

  6. Velocity and Acceleration in SHM To get the linear velocity and acceleration of an object undergoing SHM you differentiate the equation for position and then velocity, respectively

  7. The Block Spring system Remember that for a spring: Fs= -kx = ma a = -kx/m We can rewrite this as: And this means that

  8. The Block Spring system Because We can rewrite The period and frequency of a pendulum as:

  9. Practice Problem A = 4.00 m, f = .5 Hz, and T = 2.0 sec b) c) d) x = -2.83 m, v = 8.89 m/s, a = 27.9 m/s2 e) vmax = 12.6 m/s amax = 39.5 m/s2 f) x = -5.66 m An object oscillates and its position varies with time according to the equation: Find the amplitude, frequency, and period of the motion Find the velocity at any time Find the acceleration at any time Find the position, velocity, and acceleration at t = 1.0 sec Find the maximum speed and acceleration Find the displacement of the object between t = 0 and t = 1.00 sec

  10. Practice Problem A block has a mass of 2.00 kg and is connected to a spring with a spring constant k = 5.00 N/m. The block and spring sit on a frictionless horizontal surface. The block is pulled and released from rest at a position 5.00 cm from equilibrium. Find the period of the block’s motion Write an expression for the displacement, speed, and acceleration of the block at any time T = 1.26 sec x = (.05m)cos(5t) v = -(2.5 m/s)sin(5t) a = -(1.25 m/s2)cos(5t)

More Related