Suppose that a simple pendulum consists of a small 71.8 g bob at the end of a cord of negligible mass. If the angle è between the cord and the vertical is given by

è = (0.0465 rad) cos[(6.52 rad/s) t + ö],
what are (a) the pendulum's length and (b) its maximum kinetic energy?

All right, I got that l=.23053m, but I'm not sure how to get b.

To find the maximum kinetic energy of the pendulum, we need to determine the maximum velocity of the bob. Given the equation for the angle è as a function of time t:

è = (0.0465 rad) cos[(6.52 rad/s) t + ö],

we can see that the angular frequency (6.52 rad/s) determines the rate at which the angle is changing with respect to time. In other words, it tells us how fast the bob is swinging back and forth.

The maximum velocity of the bob occurs when the angle è is at its maximum value. Since we know that the maximum value of the cosine function is 1, we can set the cosine term equal to 1:

cos[(6.52 rad/s) t + ö] = 1.

Now, solve for t to find when the angle is at its maximum. Recall that the cosine function repeats itself every 2π radians, so:

(6.52 rad/s) t + ö = 0.

Solving for t gives:

t = -ö / (6.52 rad/s).

Since the cosine function is maximum at t = 0, we can simply set t = 0 and solve for the angle's maximum value:

è_max = (0.0465 rad) cos(ö).

Now that we know the maximum angle, we can determine the maximum velocity of the bob using the equation:

v_max = l * (dè / dt),

where l is the length of the pendulum and dè/dt is the derivative of the angle with respect to time.

Differentiating the given equation for the angle with respect to time:

dè / dt = -(0.0465 rad) sin[(6.52 rad/s) t + ö] * (6.52 rad/s).

At t = 0 (when the angle is at its maximum), the sine function is also maximum (equal to 1). Hence:

v_max = l * (0.0465 rad) * (6.52 rad/s) = 0.3022 l rad/s.

Now, the maximum kinetic energy of the pendulum is given by the equation:

K.E._max = (1/2) * m * v_max^2,

where m is the mass of the bob. Plugging in the values:

K.E._max = (1/2) * (0.0718 kg) * (0.3022 l rad/s)^2.

To find the value of b, you can substitute the given values into the equation and evaluate it using a calculator or computational software. The result will give you the maximum kinetic energy of the pendulum.