matlab language Write a function called pendulum that is called like this: T = p

ID: 3841238 • Letter: M

Question

matlab language

Write a function called pendulum that is called like this: T = pendulum(L,a0), where all arguments are scalars and a0 is a positive number less than . The function calculates the period T of a simple pendulum, which is the time required for a weight attached to a rod of length L and negligible weight to start from rest, swing with no friction under the influence of gravity from an initial angle a0, to – a0 and back to a0 again, as shown in the figure 1. The motion is determined by physics using the following definitions, where units [square brackets] are provided but are not needed:

= angle [radians]

1 = angular velocity [radians/s]

= angular acceleration [radians/s2]

g = acceleration due to gravity = 9.8 [m/s2]

t = time [s]

The function starts its calculation with the pendulum angle equal to a0 and then calculates a sequence of decreasing pendulum angles, each at a time separated from the one before it by t = 1 × 10-6 s. It continues until the pendulum has passed its lowest point, at which = 0. The elapsed time equals T/4.

The calculation at each time step proceeds as follows: The angular acceleration is set equal to nsin IL . Then the angular velocity 1 is increased by the product of the angular acceleration and t. That new angular velocity is then used to obtain a new by adding the product of the angular velocity and t to the old .

Here are two sample runs:

>> format long,

>> T = pendulum(2, pi/2)

T =

3.350344000012992

>> T = pendulum(0.22952, pi/4)

T =

1.000000000000917

note that : i have to get same answers and please without warnings or erros in the code

ao I a0 Figure 1 Pendulum

Explanation / Answer