Word problem in Algebra 2

Question

A weight hangs on a spring. The vibration period of that weight is the time in which it makes a complete cycle in motion. Suppose the relationship between the vibration period 'T' (in seconds) and the weight "w" (in kilograms) is given by T = 2pi√(w/200). Find the period T, to the nearest thousandth, for a spring with a hanging weight of 2.0 kilogram.

Answer 1

This problem appears to be direct substitution.

We are given the equation (with sqrt = square root, and pi = 3.1415927, approximately):

T = 2 * pi * sqrt(w / 200)

We are then asked to solve for T when w = 2.0 kg. Substituting this value in the equation, we get

T = 2 * pi * sqrt(2 / 200) = 2 * pi * sqrt( 1 / 100) = 2 * pi * (1/10) = 0.2 * pi = 0.628 seconds (rounded to the nearest thousandth).