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a complete description of simple harmonic motion must take into account several physical quantities and various mathematical relations among them. this information is needed to solve oscillation problems of this type.

the position of a 45 g oscillating mass is given by x(t)=(2.0cm)cos(10t), where t is in seconds.

a

determine the velocity at t=0.40s.

express your answer in meters per second to two significant figures.

b

assume that the oscillating mass described in part a is attached to a spring. what would the spring constant k of this spring be?

express your answer in newtons per meter to two significant figures.

c

what is the total energy e of the mass described in the previous parts?

express your answer in joules to two significant figures.

Explain in physical terms how a microwave oven works. what would happen when you put a conductor in the microwave oven? explain.

The of a machine determines its "usefulness." a. input force b. output force c. mechanical advantage

Use the frequency histogram to complete the following parts. ​(a) identify the class with the​ greatest, and the class with the​ least, relative frequency. ​(b) estimate the greatest and least relative frequencies. ​(c) describe any patterns with the data. female fibula lengths 30.5 31.5 32.5 33.5 34.5 35.5 36.5 37.5 38.5 39.5 0 0.05 0.1 0.15 0.2 0.25 length (in centimeters) relative frequency a histogram titled "female fibula lengths" has a horizontal axis labeled "length in centimeters" from 30.5 to 39.5 in increments of 1 and a vertical axis labeled "relative frequency" from 0 to 0.25 in increments of 0.05. the histogram contains vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis tick marks. the approximate heights of the vertical bars are listed as follows, where the label is listed first and the approximate height is listed second: 30.5, 0.02; 31.5, 0.04; 32.5, 0.05; 33.5, 0.13; 34.5, 0.22; 35.5, 0.25; 36.5, 0.13; 37.5, 0.06; 38.5, 0.09; 39.5, 0.01. ​(a) the class with the greatest relative frequency is nothing to nothing centimeters. ​(type integers or decimals. do not round. use ascending​ order.)