13) a pendulum of mass m, length l, amplitude a, and on the earth with acceleration due to gravity of g has a period t. how long would the pendulum need to be in order to to have a period of 2t?

4L

Explanation:

mass of pendulum = M, length of pendulum, L1 = L,

acceleration due to gravity = g, Amplitude = A

Use the formula for the time period for simple pendulum

    ..... (11)

Let the new length be L2 for which the time period is 2T.

         ..... (2)

Divide equation (2) by equation (1)

So, L2 = 4 L

Thus, the length of the pendulum is 4 L.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west

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