the spring is compressed by 7cm. How far must you compress a spring with twice the spring constant to store the same amount of energy?

if you already have the answer to (a), then just work out how many periods there are in 1 minute, and that's the answer to (c).

the aurora is formed when charged particles emitted from the sun during a solar flare penetrate the earth's magnetic shield and collide with atoms and molecules in our atmosphere. these collisions result in countless little bursts of light, called photons, which make up the aurora.

auroras are generated by charged solar particles hitting molecules in earth's atmosphere. this usually happens in high latitudes, because our planet’s magnetic field tends to funnel these particles toward the poles. that’s why it can be experienced in northern ohio.