Problem 1) A very bouncy mushroom can be modeled as mass of 30g (the mushroom cap) on top of a spring ( the mushroom stalk) with spring constant 20 N/m. A bird of mass 50g lands on the mushroom gently so that its velocity is zero when it lands. a) Relative to the initial height of the mushroom, what is the new equilibrium height of the mushroom about which oscillations will occur? b) What is the frequency of the resulting oscillations? c) What is the maximum compression of the mushroom (i.e. how far down does the cap of the mushroom go relative to its location when the bird lands) ? d) What is the equation that describes the oscillation of the mushroom as a function of time