Question

An object in SHM oscillates with a period of 4.0 s and an amplitude of 20 cm. How long does the object take to move from x = 0.0 cm to x = 7.6 cm. Express your answer to two significant figures and include the appropriate units. ∆t = ___

Answer 1

The object takes 8.0 s to move from x = 0.0 cm to x = 7.6 cm in SHM.

Step-by-step explanation:

Simple Harmonic Motion (SHM) is a repetitive, back-and-forth motion exhibited by certain systems under the influence of restoring forces. In SHM, the restoring force acting on an object is directly proportional to its displacement from a fixed equilibrium position and acts opposite to the direction of the displacement. Period refers to the time required for one complete cycle of a periodic motion, such as oscillation or vibration. In the context of Simple Harmonic Motion, the period represents the time it takes for the system to complete one full cycle of back-and-forth motion, returning to its initial position.

The object takes two periods to move from x = 0.0 cm to x = 7.6 cm in Simple Harmonic Motion (SHM). The period of the motion is given as 4.0 s. So, the time taken for one period is 4.0 s. And since the object takes two periods to complete the given displacement, the total time taken is two times 4.0 s, which equals 8.0 s.

Answer 2

the object takes approximately 0.58 s (or 0.96 s) to move from x = 0.0 cm to x = 7.6 cm.
∆t ≈ 0.58 s

The object takes approximately 0.96 s to move from x = 0.0 cm to x = 7.6 cm.

To find the time it takes for the object to move between two positions, we can use the equation:

∆t = (2π / T) * (∆x / A)

Where:
- ∆t represents the time it takes for the object to move between the two positions.
- T represents the period of the oscillation.
- ∆x represents the difference in position between the two points.
- A represents the amplitude of the oscillation.

In this case, the period (T) is given as 4.0 s and the amplitude (A) is given as 20 cm. The difference in position (∆x) is 7.6 cm.

Plugging these values into the equation, we have:

∆t = (2π / 4.0 s) * (7.6 cm / 20 cm)

Simplifying the equation, we get:

∆t ≈ 1.52 * 0.38

∆t ≈ 0.58 s