What question does Simple Harmonic Motion Calculator answer?

Calculate an ideal spring-mass oscillator's frequency, period, motion and energy at a specified time. The implemented relationship is R[simple-harmonic-motion-calculator]=ω = √(k/m); x = A cos(ωt+φ); v = −Aω sin(ωt+φ); a = −ω²x; E = kA²/2; x₁=Mass (kg); x₂=Spring constant (N/m); x₃=Amplitude (m); x₄=Elapsed time (s); x₅=Initial phase (rad).

Which inputs does Simple Harmonic Motion Calculator use?

It uses the visible fields Mass (kg), Spring constant (N/m), Amplitude (m), Elapsed time (s), Initial phase (rad). No hidden value is substituted for an omitted required input.

What happens when Simple Harmonic Motion Calculator receives an invalid or extreme value?

The page rejects missing, ambiguous, out-of-range, or non-finite values and refuses to display a non-finite result.

Why can Simple Harmonic Motion Calculator differ from another result?

Different unit conventions, endpoint policies, fee or rate assumptions, formula domains, and premature rounding can produce a different answer.

Can I use Simple Harmonic Motion Calculator as professional advice?

No. It is an educational model and is not certified engineering or safety analysis.

How can I verify the Simple Harmonic Motion Calculator result?

Recalculate the two evaluated examples without rounding intermediate values and compare the declared formula or convention with OpenStax University Physics Volume 1 — Simple Harmonic Motion.

Simple Harmonic Motion Calculator

Result0.1 m

Model and interpretation

Ideal undamped, unforced spring-mass motion: x = A cos(ωt + φ), ω = √(k/m). Mass and spring constant must be positive; phase is in radians. No friction, external driving or nonlinear spring behavior is modeled. 10⁻¹² ≤ m,k ≤ 10¹²; 0 ≤ A,t ≤ 10¹²; |φ|,|ωt+φ| ≤ 10⁸ rad.

ω (rad/s): 10
T (s): 0.628319
f (Hz): 1.59155
x (m): 0.1
v (m/s): 0
a (m/s²): -10
U (J): 0.5
K (J): 0
E (J): 0.5

Method source: OpenStax University Physics Volume 1 — Simple Harmonic Motion Report a correction

Formula

Simple Harmonic Motion Calculator evaluates the registered expression “R[simple-harmonic-motion-calculator]=ω = √(k/m); x = A cos(ωt+φ); v = −Aω sin(ωt+φ); a = −ω²x; E = kA²/2; x₁=Mass (kg); x₂=Spring constant (N/m); x₃=Amplitude (m); x₄=Elapsed time (s); x₅=Initial phase (rad)” with the validated inputs. Full calculation precision is retained until the result is formatted for display.

R[simple-harmonic-motion-calculator]=ω = √(k/m); x = A cos(ωt+φ); v = −Aω sin(ωt+φ); a = −ω²x; E = kA²/2; x₁=Mass (kg); x₂=Spring constant (N/m); x₃=Amplitude (m); x₄=Elapsed time (s); x₅=Initial phase (rad)

OpenStax University Physics Volume 1 — Simple Harmonic Motion

What this calculator answers

Simple Harmonic Motion Calculator applies the registered method “ω = √(k/m); x = A cos(ωt+φ); v = −Aω sin(ωt+φ); a = −ω²x; E = kA²/2” to the displayed Mass (kg), Spring constant (N/m), Amplitude (m), Elapsed time (s), Initial phase (rad) inputs. Both worked examples come from the production calculation engine, and OpenStax University Physics Volume 1 — Simple Harmonic Motion defines the cited method or convention; no hidden inputs or current external data are inferred.

Variables, defaults, and limits

Mass (kg): Mass (kg) is a number input. The displayed starter value is 1; it is an example, not a hidden assumption.; Default: 1; Accepted values: Allowed range: 0.000000000001 to 1,000,000,000,000. Numeric entries must be finite and unambiguous.
Spring constant (N/m): Spring constant (N/m) is a number input. The displayed starter value is 100; it is an example, not a hidden assumption.; Default: 100; Accepted values: Allowed range: 0.000000000001 to 1,000,000,000,000. Numeric entries must be finite and unambiguous.
Amplitude (m): Amplitude (m) is a number input. The displayed starter value is 0.1; it is an example, not a hidden assumption.; Default: 0.1; Accepted values: Allowed range: 0 to 1,000,000,000,000. Numeric entries must be finite and unambiguous.
Elapsed time (s): Elapsed time (s) is a number input. The displayed starter value is 0; it is an example, not a hidden assumption.; Default: 0; Accepted values: Allowed range: 0 to 1,000,000,000,000. Numeric entries must be finite and unambiguous.
Initial phase (rad): Initial phase (rad) is a number input. The displayed starter value is 0; it is an example, not a hidden assumption.; Default: 0; Accepted values: Allowed range: -100,000,000 to 100,000,000. Numeric entries must be finite and unambiguous.

Formula and calculation rule

R[simple-harmonic-motion-calculator]=ω = √(k/m); x = A cos(ωt+φ); v = −Aω sin(ωt+φ); a = −ω²x; E = kA²/2; x₁=Mass (kg); x₂=Spring constant (N/m); x₃=Amplitude (m); x₄=Elapsed time (s); x₅=Initial phase (rad)

Worked examples