Use your kinematic equations. Start by writing what you know (initial velocity is 0, time is 0.3 seconds, and distance traveled can be measured from the drawing).
Once you know three things, you can use your kinematic equations to solve for the other two (details here: https://www.aplusphysics.com/courses/regents/videos/KinEqns_Reg/KinEqns_Reg.html)

Hi Terry -- based on popular request of instructors I don't give out the solutions to the lab, leaving it to instructors to formulate their solutions (otherwise it becomes a much less effective tool for classroom teachers as students could just copy the answers).

Graphing the empirical k_delta_x vs. Msintheta would work, but not the theoretical. They want you to determine an empirical value for g, not do a mathematical exercise that results in a 1=1 proof.

I might start with a resource like this: https://opentextbc.ca/physicstestbook2/chapter/damped-harmonic-motion/ or this: https://www.toppr.com/guides/physics/oscillations/damped-simple-harmonic-motion/

Hi Muskkan. Damped oscillators are outside the scope of AP Physics 1/2, but happy to help if I can. How far have you gotten so far / where are you getting stuck?

Correct. When you purchase the book it specifically says it cannot be printed (part of the licensing deal with publishers). However, all of the question sets are available to print individually at https://www.aplusphysics.com/courses/regents/worksheets/ws_index.html.