2d and 2f answered please Transcription and Explanation for Educational Context:---**Pendulum Motion Analysis**3) The angle of the pendulum from straight down will vary in a sinusoidal fashion as it swings. In Physics, you will learn (if you haven’t already) that for a frictionless pendulum, released \( k \) radians from vertical, the angle will be:\[\theta(t) = k \cos\left(\sqrt{\frac{g}{L}} \cdot t\right)\]- \( g \) is gravitational acceleration; on Earth's surface, \( g \approx 32 \, \text{feet/s}^2 \).- For our problem, the pendulum length \( L \) is 20 inches, which must be converted to feet for the equation.- We will use \( k = 0.15 \) radians.**Tasks:**a. **Find the angular frequency (\(\omega\)) of the oscillation.**b. **Find the period in seconds.**c. **Find the time until \(\theta(t) = 0\)** (i.e., when it is straight down).d. **Plot one complete cycle of the waveform by hand.** Be sure to label the amplitude and period on the plot.e. **Using a software tool, confirm your calculations and plot the function over one cycle.** Confirm that it agrees with your hand plot.f. **Suppose we had chosen to write the pendulum equation using a sine function instead of a cosine.** What phase offset would we have to add to get the same behavior?**Illustration:**The diagram depicts a pendulum with a length \( L = 20 \) inches and an initial displacement angle \( \theta = 0.15 \) radians from the vertical.---**Graph Explanation:**The graph is expected to be a sine wave representing the pendulum’s angular displacement over time, with labels on amplitude (maximum angle reached from equilibrium) and period (time for one complete oscillation).

The angle of pendulum from straight down will vary in a sinusoidal fashion as it swings. In Physics you will learn (if you haven't already) that for a frictionless pendulum, released k radians from feet vertical will be 0 (t) = k cos (t). g is gravitational acceleration, on Earth's surface~32 s2 %3D For our problem the length is 20 inches, which will require conversion to be the L in the equation. We will use k = 0.15 radians.