# Math Help - sinusoidal applications and the derivative

1. ## sinusoidal applications and the derivative

Please help with these questions:

1.A marble is placed on the end of a horizontal oscillating spring. For the given signal determine:
i) the period, T, in seconds
ii)the frequency, f, in hertz
iii) the amplitude, A, in volts

2. consider a simple pendelum that has a length of 50cm and a maximum horizontal displacement of 8cm.
a) find the period of the pendelum
b) determine a function that gives the horizontal position of the bob as a function of time
c) determine a function that gives the velocity of the bob as a function of time
d) determine a function that gives the acceleration of the bob as a function of time

My teacher said that the horizontal position is also the displacement function; the velocity is the derivative of the displacement function and acceleration is the derivative of the velocity function. Please clarify. Thanks.

2. ## Re: sinusoidal applications and the derivative

1) Which signal are you given? The Period is just the amount of time that a function repeats itself. For example $\sin(t)$ has period $T=2\pi$ because $\sin(t)=\sin(t+2\pi)$

2) Do you know the equation of the period of a pendulum? In the small angle approximation (which is the approximation that you're using) it is a very simple function of its length. Once you have the function that gives the horizontal position, their first and second time derivatives will give you the velocity and acceleration respectively. Because it is their definition, the velocity is the time derivative of the position, and the acceleration is the time derivative of the velocity.

3. ## Re: sinusoidal applications and the derivative

For 1. i've included a picture of the question from the textbook. in regards to the given signal, i'm not sure if the question is referring to the picture of the purple marble on the end of the horizontal spring.

For 2. the back fo the textbook says the period is 1.412 seconds. But I'm still confused as to how they got that. Please clarify.