Simple Question About Pendulum I Can't Do

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In summary, the given equation describes the motion of a pendulum's bob where theta is the angle from vertical. The question asks for the amplitude of this motion, which can be found by determining the maximum value of the function.
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tweety_2479
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Simple Question About Pendulum I Can't Do !

The motion of the bob of a pendulum is described by

theta = 3cos(3t) - sqrt3 sin(3t)

where theta is the angle of the bob from the vertical. What is the amplitude of this motion??

as an attempt, as i know what the answer is, but just don't know how to get to it i substituted the answer for theta and tried to find what t was
but it didnt help i don't really no where to start for this probelm

thanks if youcould help
 
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HINT: How do you find the maximum of a function?
 
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I would approach this problem by first understanding the equation for the motion of a pendulum. The equation given in the problem is a simplified form of the equation for a simple harmonic motion, which is the type of motion exhibited by a pendulum. The equation is theta = A cos(wt + phi), where A is the amplitude, w is the angular frequency, and phi is the phase angle.

To find the amplitude in this equation, we need to identify the value of A. In this case, we can see that A = 3, as it is the coefficient of the cosine term. This means that the amplitude of the pendulum's motion is 3 units. This can also be confirmed by graphing the equation and observing the maximum and minimum values of theta.

To further understand the equation, we can also note that the angular frequency, w, is equal to 3 in this case. This means that the pendulum completes 3 full cycles in one second. The phase angle, phi, is not given in the problem, but it does not affect the amplitude of the motion.

In summary, the amplitude of the motion of the pendulum is 3 units. To solve this problem, it is important to understand the equation for simple harmonic motion and identify the values of A, w, and phi.
 

What is a pendulum?

A pendulum is a weight suspended from a fixed point that is able to swing freely back and forth under the influence of gravity.

What factors affect the motion of a pendulum?

The motion of a pendulum is affected by its length, weight, and the strength of the gravitational force acting on it.

How does the length of a pendulum affect its period?

The length of a pendulum directly affects its period, or the time it takes for one complete swing. A longer pendulum will have a longer period, while a shorter pendulum will have a shorter period.

What is the formula for calculating the period of a pendulum?

The formula for calculating the period of a pendulum is T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

How can pendulums be used in scientific experiments?

Pendulums can be used in scientific experiments to study the effects of gravity, to measure time, and to demonstrate principles of oscillation and energy conservation. They are also commonly used in timekeeping devices such as clocks.

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