A 2 kg block attached to a spring with spring constant 8 N/m is displaced 2 m from equilibrium and released. What is the time it takes to reach 1 m from equilibrium?

The angular frequency for a mass-spring system is given by the formula:

Given $m = 2 \text{ kg}$ and $k = 8 \text{ N/m}$:

Assuming the block is released from its maximum displacement $A = 2 \text{ m}$ at $t=0$, the position $x(t)$ is given by:

We want to find the time $t$ when $x = 1 \text{ m}$.

Take the inverse cosine of both sides:

We know that $\arccos\left(\frac{1}{2}\right) = \frac{\pi}{3} \text{ rad}$.

None of the options (A. 40 sec B. 60 sec C. 30 sec D. 20 sec) match this result. There might be an issue with the question's options or interpretation. However, based on the standard SHM model, this is the time taken. If the question implies traveling to $x=1$ from $x=2$ and then back to $x=1$ or some other interpretation, it's not explicitly stated. Assuming the simplest interpretation of starting at $x=2$ and moving towards $x=0$.

The final answer is $\boxed{\text{0.52 s}}$.

The frequency of the simple pendulum is $f = 1.5 \text{ Hz}$.

The relationship between angular frequency $\omega$ and frequency $f$ is:

Substitute the given frequency:

The final answer is $\boxed{\text{B. } 3.0\pi}$.

Damping of periodic motion always results in a decrease in the amplitude of the oscillations over time due to energy dissipation.

The final answer is $\boxed{\text{B. decreasing amplitude}}$.

Total mass $M = m_{car} + m_{passengers}$

Since there are four springs supporting the car, and they are in parallel, the total effective spring constant $k_{total}$ is the sum of the individual spring constants.

The angular frequency for a mass-spring system is given by:

The frequency $f$ is related to the angular frequency $\omega$ by:

Comparing this to the given options:
A. $2.31 \text{ Hz}$
B. $1.42 \text{ Hz}$
C. $5.36 \text{ Hz}$
D. $1.18 \text{ Hz}$

The calculated frequency is approximately $1.18 \text{ Hz}$.

The final answer is $\boxed{\text{D. } 1.18 \text{ Hz}}$.