Question

How is the motion of a physical pendulum different than that of a simple pendulum? Can the characteristics of simple harmonic motion be used to characterize the motion of physical pendulum – amplitude, period, and angular frequency? Consider the chaotic physical pendulum. Be able to describe the relationship between the phase plot and the time series graph for a chaotic oscillator. Can you look at a segment of a time series graph and describe what an oscillator is doing in words?

Answer 1

Ans).1&2q.Ans).

Simple Pendulum:

A simple pendulum is one which can be considered to be a point mass suspended from a string or rod of negligible mass. It is a resonant system with a single resonant frequency. For small amplitudes, the period of such a pendulum can be approximated by:

5 T =2π Show For pendulum length L =  cm = m and acceleration of gravity g = m/s2 the pendulum period is T =  sec Note that the angular amplitude does not appear in the expression for the period. This expression for period is reasonably accurate for angles of a few degrees, but the treatment of the large amplitude pendulum is much more complex. Pendulum Motion: The motion of a simple pendulum is like simple harmonic motion in that the equation for the angular displacement is e_.sin.f max Show which is the same form as the motion of a mass on a spring: ASin_t The anglular frequency of the motion is then given by compared to Im for a mass on a spring. The frequency of the pendulum in Hz is given by and the period of motion is then T = 2π Pendulum Geometry: The period of a simple pendulum for small amplitudes ? is dependent only on the pendulum length and gravity. For the physical pendulum with distributed mass, the distance from the point of support to the center of mass is the determining "length" and the period is affected by the distribution of mass as expressed in the moment of inertia I. Simple Pendulum Physical: Pendulum cm Tension cm mg sin θ mgła ng cos θ mg sin θ mg

3qA).By using data analysis, such as the phase plot (continuous velocity vs. position), the Poincare plot (periodic velocity vs. position), and the potential energy plot (energy vs. position), we can make reasonable predictions about how a system will act by observing the patterns of motion around the fixed points.

4q.A).An oscillator is an indicator that fluctuates above and below a centerline or between set levels as its value changes over time. Oscillators can remain at extreme levels (overbought or oversold) for extended periods, but they cannot trend for a sustained period. In contrast, a security or a cumulative indicator like On-Balance-Volume (OBV) can trend as it continually increases or decreases in value over a sustained period of time.

-MACD(12,26,9) 0.363, 0.202, 0.161 1.00 0.75 0.50 0.25 0.00 -0.25 0.50 0.75 1.00 -On Balance Vol -MA(30) J A SON D 03 F M A M JJ A S ON D 04 F M A M J

As the indicator comparison chart shows, oscillator movements are more confined and sustained movements (trends) are limited, no matter how long the time period.