1)1.A hanging spring is stretched by 0.2 m when a mass of 0.5 kg is attached to it. The mass is then pulled down a further 0.1 m and released from rest.a)What is the angular frequency of the resulting oscillations? Show your work.b)How many seconds does it take for the system to go through exactly 10 complete oscillations? Show your work.

2)Taking y = 0 as the initial equilibrium position of the mass in Question 1, and y > 0 upwards, write down an equation for the time dependence y(t), giving the numerical values of any constants in the solution.

3)What is the velocity of the mass in Questions 1 and 2 as it oscillates through the equilibrium point y = 0? (Hint: you could use your solution to Question 2 to get this, or equivalently you could use conservation of energy)

4)In the case of a pendulum system, what exactly about the system is oscillating in time? What physical parameters could you change in the system that might change the oscillation frequency? (i.e. what could you investigate if you didn't know the answer.)