https://file.aiquickdraw.com/mathbot/file/1726097188017uvxte9ww.jpg

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).

1) Un bloque de 2000 gramos está sujeto a un resorte en reposo cuya constante k=150N/m. Calcular el periodo y la frecuencia de la masa cuando se le aparta de la posición de equilibrio. 2) Una partícula presenta un desplazamiento dado por la expresión: x = (3.2m) * cos (9.32π * t + π/2). Donde x está en metros y t en segundos, calcular: La amplitud del movimiento, la frecuencia angular, la frecuencia, el periodo y el desplazamiento de la partícula en el tiempo t = 1.3 s. 3) Investigue y describa que son los movimientos ondulatorios en la física.

Learn how to calculate the period and frequency of a spring system with a 2000g block and k=150N/m constant. Also, explore the amplitude, frequency, angular frequency, and displacement of a particle with given motion. Includes step-by-step solutions suitable for students in Grades 10-12.

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