Show your work.

1) A mass m is connected to a spring with spring constant k on a frictionless horizontal surface, and is oscillating with angular frequency w = 2.4 rad/s. At t = O, the position of the mass is a: = O.21 m (the equilibrium position is taken to be :1: = O), and has a velocity 'v = 1.3 m/s. What will be the position and velocity of this mass at t = 1.0 s? a) Both springs are now connected to the mass as below. What is the angular frequency of the resulting oscillations? b) Same as part a, but now the springs are connected as below.2) Consider two springs with spring constants 1:1 and 162. When the rst spring (only) is connected to a mass m on a frictionless horizontal surface, the mass oscillates with angular frequency LL21. When the second spring (only) is connected to the same mass, the mass oscillates with angular frequency Lag. 3) The potential energy of a 10 g mass is given as a function of its position by U(x) = (5 J) ex/(1cm) + (2J) e-3x/(1 cm) a Find the equilibrium position Teq. b) For small displacements around x = Weg, find the period of oscillations.