A toy dart gun contains a spring with a spring constant of 250 N/m. A 0.059 kg dart is pressed 0.050 m into the gun.

a) If the gun is aimed directly upward, how high into the air will the dart travel when shot (measured from the compressed position in the gun)?

b) What is the maximum velocity of the dart?

c) If the dart got stuck to the spring:

i) with what angular frequency will the dart oscillate (neglect friction)?

ii) with what frequency will the dart oscillate (neglect friction)?

iii) what will be the period of this oscillation?