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The frequency of oscillation of an object suspended on a spring depends on the stiffness k of the spring (called the spring constant) and the mass m of the object. If the spring is compressed a distance a and then allowed to oscillate, its displacement from its starting point is given by
f(t) = a cos√(k/mt)
a) A mass of 10g is suspended from a spring with stiffness k = 3. If the spring is compressed a distance 5 cm and then released, find the equation that describes the oscillation of the spring.
b) Find a general formula for its frequency of oscillation (in terms of k and m).
c) How is the frequency affected if the mass is increased? Is the oscillation faster or slower?
d) How is the frequency affected if a stiffer spring is used (larger k)? Is the oscillation faster or slower?
ABCD is a rectangle. Δ ADE and Δ ABF are two triangles such that ∠E=∠F as shown in the figure. Prove that AD x AF=AE x AB. Ans: Consider Δ ADE and Δ ABF ∠D = ∠B
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Determine the measure of the vertex angle of the isosceles triangle. a. 34° b. 16° c. 58° d. 112° d. Simply substitute x = 34 into the equation for the vertex angle,
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