# Thread: 3 Bad Hard Problems

1. ## 3 Bad Hard Problems

The period T of a clock pendulum (i.e., the time required for one back and forth movement) is given in terms of its lenght L by the equation:
T = [2PI][sqrt L/G], where g is the gravitational constant.

a) Assuming that the lenght of a clock pendulum can vary (say, due to temperature changes), find the rate of change of the period T with respect to the lenght L.

b) If L is in meters (m) and T is in seconds (s), what are the units of the rate of change in part (a)?

c) If a pendulum clock is running slow, should the lenght of the pendulum be increased or decreased to correct the problem?

To me, this tough. Please Help Me solve these problems Please.
Thanks in advance to anyone who help

2. Originally Posted by Collegegirl88
The period T of a clock pendulum (i.e., the time required for one back and forth movement) is given in terms of its lenght L by the equation:
T = [2PI][sqrt L/G], where g is the gravitational constant.
$\displaystyle T= 2\pi \sqrt{L/G}= 2\pi L^{1/2}G^{-1/2}$.

a) Assuming that the lenght of a clock pendulum can vary (say, due to temperature changes), find the rate of change of the period T with respect to the lenght L.
Find the derivative of T with respect to L, treating G as a constant. What is the derivative of $\displaystyle x^n$ for any real number, n?

b) If L is in meters (m) and T is in seconds (s), what are the units of the rate of change in part (a)?
The derivative is the limit of a fraction: T(L+h)-T(L)/h If T is in seconds and L and h are in meters, what units does that fraction have?

c) If a pendulum clock is running slow, should the lenght of the pendulum be increased or decreased to correct the problem?
Assuming that T and G are positive, is the derivative in (a) positive or negative? If it is positive, that means decreasing the length will decrease the period and so make the clock run faster. If it is negative, that means increasing the length will decrease the period and so make the clock run faster.

To me, this tough. Please Help Me solve these problems Please.
Thanks in advance to anyone who help

3. I know where u going with the steps but I am still lost on what u saying

4. Do you read up on any of the concepts that the problems involve? I would suggest reading up the section of your book that contain's this so you can get some idea of what to do, if you do not know how to do the the steps how to do the problems go back to the basics, understanding derivatives and etc.