NEED HOMEWORK HELP Mass/Spring/Pendulum system

[ss883]

Homework Statement

The figure below shows a pendulum of length L with a bob of mass M. The bob is attached to a spring that has a force constant k. When the bob is directly below the pendulum support, the spring is unstressed. Derive an expression for the period of this oscillating system for small-amplitude vibrations (assume there is no displacement from the horizontal). Suppose that M = 1.80 kg and L is such that in the absence of the spring the period is 2.90 s. What is the force constant k if the period of the oscillating system is 1.45 s?

2. The attempt at a solution

Tpendulum = 2pi*\sqrt{L/g}
then L= 2.089 m

...I seriously have no idea what to do next please help asap.

 

[rock.freak667]

I think essentially what they are asking for is that when the pendulum collides with the spring, the mass sticks to the spring and then it oscillates. So it is essentially just a mass on a spring. In that case you can the expression for the force on a spring to get the SHM equation for it. (Start by writing how force relates to extension and spring constant, then apply Newton's 2^nd law)

 

[ss883]

...can you try to solve it? When I say I have no idea how to do this problem, I mean I really don't get it.

Or at least give me a formula/derivation

 

[rock.freak667]

...can you try to solve it? When I say I have no idea how to do this problem, I mean I really don't get it.

Or at least give me a formula/derivation

Do you know how to derive equations of motion using energy methods or by using Newton's second law?

For both methods you need to draw a free-body diagram. So start with that.