Question

The position of a 50 g oscillating mass is given by g a(t) = (2.0 cm)cos(10t – 1/4), where t is in s. If necessary, round your answers to three significant figures. Determine: Part B The period. Express your answer with the appropriate units.Part D The phase constant. Express your answer with the appropriate units.

Answer 1

Part B: The period of the oscillation can be determined from the angular frequency (\(ω\)) in the equation \(ω = \frac{2π}{T}\), where \(T\) is the period. In your given equation \(a(t) = (2.0 cm)\cos(10t – \frac{1}{4})\), the angular frequency is 10 (as it appears in front of \(t\)).

So, plug in the values and solve for \(T\):

\[10 = \frac{2π}{T}\]

Solving for \(T\):

\[T = \frac{2π}{10} = \frac{π}{5} \approx 0.628 \text{ s}\]

Part D: The phase constant is the value that appears in the argument of the cosine function. In this case, it's \(-\frac{1}{4}\), but to express it in appropriate units, we'll use radians. Since there are \(2π\) radians in a full cycle, we can convert it to radians:

\[-\frac{1}{4} \text{ cycles} = -\frac{1}{4} \cdot 2π \text{ radians} = -\frac{π}{2} \text{ radians}\]

Therefore, the phase constant is \(-\frac{π}{2}\) radians.