Let's go over the problems in the image one by one.

Problem 1:

A block of 2000 grams is attached to a spring with a constant $k = 150 \, \text{N/m}$. Calculate the period and frequency of the mass when displaced from equilibrium.

To solve this:

1. The mass of the block is given as $2000 \, \text{g} = 2 \, \text{kg}$ (since $1000 \, \text{g} = 1 \, \text{kg}$).
2. The spring constant $k = 150 \, \text{N/m}$.

The period $T$ of a mass-spring system in simple harmonic motion is given by: $T = 2\pi \sqrt{\frac{m}{k}}$ where:

• $m$ is the mass (in kg),
• $k$ is the spring constant.

The frequency $f$ is the reciprocal of the period: $f = \frac{1}{T}$

Now, substituting the given values: $T = 2\pi \sqrt{\frac{2}{150}}$ $f = \frac{1}{T}$

Let me calculate the exact values.

Problem 2:

A particle’s displacement is given by the equation: $x = (3.2 \, \text{m}) \cdot \cos\left(9.32\pi \cdot t + \frac{\pi}{2}\right)$ where $x$ is in meters and $t$ is in seconds. You are asked to calculate:

• The amplitude of the motion.
• The angular frequency $\omega$.
• The frequency $f$.
• The period $T$.
• The displacement of the particle at $t = 1.3 \, \text{s}$.

Amplitude: From the equation, the amplitude $A = 3.2 \, \text{m}$.

Angular frequency: The angular frequency $\omega$ is the coefficient of $t$ in the argument of the cosine, i.e., $9.32\pi \, \text{rad/s}$.

Frequency $f$ is related to angular frequency by: $f = \frac{\omega}{2\pi}$

Period $T$ is the reciprocal of the frequency: $T = \frac{1}{f}$

Finally, to find the displacement at $t = 1.3 \, \text{s}$, substitute $t = 1.3$ into the given equation and solve for $x$.

Problem 3:

Investigate and describe what wave motions are in physics.

Wave motion in physics refers to the transfer of energy through oscillations or disturbances in a medium or space. This can happen without the transfer of matter. Examples include sound waves (mechanical waves) and light waves (electromagnetic waves).

Now, let me calculate the results for Problems 1 and 2.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can still calculate these manually:

1. For Problem 1, use the formula: $T = 2\pi \sqrt{\frac{m}{k}}$ with $m = 2 \, \text{kg}$ and $k = 150 \, \text{N/m}$, and then find $f = \frac{1}{T}$.

2. For Problem 2, apply:

   • $f = \frac{\omega}{2\pi}$, where $\omega = 9.32\pi$.
   • Then find $T = \frac{1}{f}$.
   • To compute displacement at $t = 1.3$, substitute $t = 1.3$ into the expression: $x = (3.2) \cos\left(9.32\pi \cdot t + \frac{\pi}{2}\right)$

If you'd like more help, feel free to ask!

Relative questions:

1. What are the assumptions behind the formula for the period of a mass-spring system?
2. How is angular frequency different from regular frequency?
3. What other factors can affect the period of oscillation in real-life situations?
4. How would you calculate the energy stored in the spring system?
5. What happens to the period and frequency if the spring constant doubles?

Tip: For simple harmonic motion problems, always check units carefully to ensure consistency (especially between mass, spring constant, and time).