Ch 14: Periodic Motion

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경

Young & Freedman Calc 14th Edition

Ch 14: Periodic Motion

문제 11

14장, 문제 11

An object is undergoing SHM with period 0.900 s and amplitude 0.320 m. At t = 0 the object is at x = 0.320 m and is instantaneously at rest. Calculate the time it takes the object to go (a) from x = 0.320 m to x = 0.160 m. (b) from x = 0.160 m to x = 0.

검증된 단계별 안내

Step 1: Understand the problem. The object is undergoing Simple Harmonic Motion (SHM) with a given period and amplitude. At t = 0, the object is at its maximum displacement (amplitude) and is momentarily at rest. We need to calculate the time taken for the object to move between specified positions.

Step 2: Recall the equation for SHM. The displacement x as a function of time t can be expressed as:

x = A \cos (ω t + φ)

, where A is the amplitude,

ω

is the angular frequency, and

φ

is the phase constant.

Step 3: Calculate the angular frequency

ω

. The angular frequency is related to the period T by the formula:

ω = \frac{2 π}{T}

. Substitute the given period to find

ω

Step 4: Determine the phase constant

φ

. Since the object is at rest at its maximum displacement at t = 0, the phase constant

φ

is 0, because

\cos (φ)

must equal 1.

Step 5: Solve for the time intervals. (a) Use the SHM equation to find the time when the object is at x = 0.160 m. Set

x

to 0.160 m and solve for t. (b) Repeat the process for x = 0, starting from x = 0.160 m. Use the SHM equation to find the time taken for this interval.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

10m

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Simple Harmonic Motion (SHM)

Simple Harmonic Motion is a type of periodic motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. It is characterized by sinusoidal oscillations, with parameters such as amplitude, period, and frequency defining the motion's specifics.

Amplitude

Amplitude in SHM refers to the maximum displacement of the object from its equilibrium position. It is a measure of the energy in the system and determines the extent of oscillation. In this problem, the amplitude is 0.320 m, indicating the furthest point the object reaches from the center of its motion.

Period

The period of SHM is the time taken for one complete cycle of motion. It is inversely related to frequency and is a crucial factor in determining the timing of oscillations. Here, the period is 0.900 s, which helps calculate the time intervals for specific displacements during the object's motion.