could you please solve the Theoretical and Experimental tasks of PHYS105 part?

Simple Pendulum Figure 1. Principle scheme of the experimental setup. Consider the string to be massless, such that all mass of the pendulum is represented with the bob mass m. Remark: An oscillation is a motion that characterized by repeatability over time of physical values quantities (the angle of deviation from the vertical line in our case) that determine movement or state. Oscillations are called periodic if the value versus time t changes such that the oscillation process is repeated through an equal period T of time: (t+T)=(t). Mathematical model: Let's consider the simplified model where the force returning the pendulum to the equilibrium position is linear with respect to the deviation angle : Freturn=k, with some positive constant k. Then the equation of motion for the pendulum is given in the form of a second derivative term and the function itself: dt2d2(t)+2(t)=0. Here the frequency =1/T. PHYS105 Theoretical Task: 1. Derive the equation for the kinetic energy K(t), potential gravity energy U(t) and the mechanical energy E(t)=K(t)+U(t). 2. What can you say about the mechanical energy E conservation for the model (2)? 3. Analyzing units, find how the pendulum frequency depends on the following parameters: m, L,max and g (the gravity acceleration). 4. What is the physical meaning of B in Eq.(3)? 5. How the period T of the pendulum oscillation depends on m and L ? PHYS105 Experimental Task: Install the experimental setup and track the oscillations of the bob as function (t). 1. Make a conclusion if the real (t) follows Eq.(3) or not. 2. Evaluate the mechanical energy conservation for your experimental setup. If the mechanical energy is not conserved then evaluate the average % of its losing per a single period. For the tasks 1-2, one period could be too short for practical measurement, you are recommended to observe the system a longer time (like 10T) and repeat your evaluation few times. 3. Explain the difference in the behavior of a real pendulum and the theoretical solution (3). What could be the reason for that