1 The displacement of an oscillating mechanism (in $$ m $$ ) at any time ( $$ t $$ seconds) is given by $$ y=-30 \cos (3 \pi t-0.35) $$.

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The given displacement function for the oscillating mechanism is:

$$
y = -30 \cos(3 \pi t - 0.35)
$$

This equation describes a cosine wave, which can be analyzed in terms of its amplitude, angular frequency, phase shift, and period.

### Key Characteristics:

1. **Amplitude**:
   The amplitude of the oscillation is the coefficient in front of the cosine function. Here, the amplitude $$ A $$ is:
   $$
   A = 30 \, \text{m}
   $$

2. **Angular Frequency**:
   The angular frequency $$ \omega $$ is the coefficient of $$ t $$ inside the cosine function. In this case:
   $$
   \omega = 3 \pi \, \text{rad/s}
   $$

3. **Phase Shift**:
   The phase shift $$ \phi $$ can be found from the term $$ -0.35 $$ in the cosine function. The phase shift is given by:
   $$
   \phi = \frac{-0.35}{\omega} = \frac{-0.35}{3 \pi} \, \text{radians}
   $$

4. **Period**:
   The period $$ T $$ of the oscillation can be calculated using the formula:
   $$
   T = \frac{2\pi}{\omega} = \frac{2\pi}{3\pi} = \frac{2}{3} \, \text{seconds}
   $$

### Summary:
- **Amplitude**: $$ 30 \, \text{m} $$
- **Angular Frequency**: $$ 3 \pi \, \text{rad/s} $$
- **Phase Shift**: $$ \frac{-0.35}{3 \pi} \, \text{radians} $$
- **Period**: $$ \frac{2}{3} \, \text{seconds} $$

If you have any specific questions or need further analysis regarding this oscillating mechanism, feel free to ask!
The displacement function for the oscillating mechanism is $$ y = -30 \cos(3 \pi t - 0.35) $$. Its key characteristics are: amplitude $$ 30 \, \text{m} $$, angular frequency $$ 3 \pi \, \text{rad/s} $$, phase shift $$ \frac{-0.35}{3 \pi} \, \text{radians} $$, and period $$ \frac{2}{3} \, \text{seconds} $$.

1 The displacement of an oscillating mechanism (in \( m \) ) at any time ( \( t \) seconds) is given by \( y=-30 \cos (3 \pi t-0.35) \).

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