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12.81 Simple Harmonic Motion Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Physics Science worksheet provides structured practice on 12.81 Simple Harmonic Motion. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Simple Harmonic Motion: Identify displacement, velocity, acceleration, and restoring force patterns in simple harmonic motion. Aligned to NGSS, CCSS Literacy and Mathematics, AP Physics, and selected state frameworks 12.81 - Simple Harmonic Motion: NGSS HS-PS4-1, HS-PS4-2, HS-PS4-3, HS-PS4-4, HS-PS4-5; CCSS HSN-Q.A, HSF-IF, HSG-MG, RST.11-12.7; AP Physics 1 oscillations; AP Physics 2 waves, sound, physical optics, geometric optics; TX TEKS Physics §112.45(c) waves/light; FL SC.912.P.10, SC.912.P.12; VA PH.5/PH.7; MA/CA/NY HS-PS4.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Physics

Subject

Science

Domain

Science Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related 12.81 Simple Harmonic Motion skill assessments:

Problem 1Difficulty: Mastery

Use the simulator outputs shown. Which output best supports the claim that the motion is simple harmonic?

AAn a-versus-x plot that is a straight line with negative slope through the origin.

BA speed-versus-time plot that is always zero.

CA force-versus-time plot that never changes sign.

DA displacement-versus-time plot that jumps randomly between positions.

Solution & Explanation:The strongest evidence for SHM is a linear restoring acceleration pattern, a = -omega² x, shown by a negative-slope a-versus-x line through the origin.

Problem 2Difficulty: Mastery

Use the full-cycle summary shown. Which statement correctly describes the SHM pattern across one cycle?

AForce and acceleration are in phase with each other and opposite displacement.

BForce is in phase with displacement and opposite acceleration.

CVelocity is zero at equilibrium and maximum at turning points.

DAcceleration is zero at turning points and maximum at equilibrium.

Solution & Explanation:The net restoring force and acceleration point in the same direction. Both are proportional to -x and therefore opposite displacement.

Problem 3Difficulty: Mastery

If a(t) is at its positive maximum at time t0, what are x(t0) and v(t0)?

Ax is maximum positive and v = 0.

Bx = 0 and v is maximum positive.

Cx is maximum negative and v = 0.

Dx = 0 and v is maximum negative.

Solution & Explanation:Positive maximum acceleration occurs at maximum negative displacement. At either turning point, velocity is zero.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Physics Science students. It aligns with educational standard 12.81 (NGSS HS-PS4-1, HS-PS4-2, HS-PS4-3, HS-PS4-4, HS-PS4-5; CCSS HSN-Q.A, HSF-IF, HSG-MG, RST.11-12.7; AP Physics 1 oscillations; AP Physics 2 waves, sound, physical optics, geometric optics; TX TEKS Physics §112.45(c) waves/light; FL SC.912.P.10, SC.912.P.12; VA PH.5/PH.7; MA/CA/NY HS-PS4.).