Energy conservation in simple harmonic motion:

$\overline{){\mathbf{E}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{k}}{{\mathbf{A}}}^{{\mathbf{2}}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{\mathbf{\left(}}{{\mathbf{v}}}_{\mathbf{m}\mathbf{a}\mathbf{x}}{\mathbf{\right)}}}^{{\mathbf{2}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{k}}{{\mathbf{x}}}^{{\mathbf{2}}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{\mathbf{\left(}{\mathbf{v}}_{\mathbf{x}}\mathbf{\right)}}^{{\mathbf{2}}}}$

This problem involves the simple harmonic motion of springs.

We'll apply the conservation of energy to relate the speed and positions.

A 0.600 kg block is attached to a spring with spring constant 15 N/m. While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 44 cm/s.

(a) What is the amplitude of the subsequent oscillations? Answer should be in cm.

(b) What is the block's speed at the point where x = 1/4 A? Answer should be in cm/s.

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Intro to Simple Harmonic Motion (Horizontal Springs) concept. You can view video lessons to learn Intro to Simple Harmonic Motion (Horizontal Springs). Or if you need more Intro to Simple Harmonic Motion (Horizontal Springs) practice, you can also practice Intro to Simple Harmonic Motion (Horizontal Springs) practice problems.