Spring-Mass and Pendulum Systems
A spring-mass system oscillates with T = 2 π √(m/k), a simple pendulum with T = 2 π √(l/g) for small angles.
What is Spring-Mass and Pendulum Systems?
A spring-mass system oscillates with T = 2 π √(m/k), a simple pendulum with T = 2 π √(l/g) for small angles.
Key formula / rule: Spring: T = 2 π √(m/k); series and parallel springs change k.
Key points
- Derive the time period of spring-mass and pendulum systems.
- Apply effective gravity to pendulums in accelerating frames.
Common exam trap
Using the pendulum formula at large amplitude.
Definitions
- Term
Spring-Mass and Pendulum Systems
- Meaning
A spring-mass system oscillates with T = 2 π √(m/k), a simple pendulum with T = 2 π √(l/g) for small angles.
- Term
Spring-Mass and Pendulum Systems — explanation
- Meaning
Both results follow from matching the restoring force to the SHM condition. The pendulum result assumes small amplitude, where sin t is approximately t.
Learning objectives
Derive the time period of spring-mass and pendulum systems.
Apply effective gravity to pendulums in accelerating frames.
Formulae
- Key point
Spring: T = 2 π √(m/k); series and parallel springs change k.
- Key point
Pendulum: T = 2 π √(l/g), independent of mass and amplitude for small angles.
- Key point
In a lift, replace g by the effective acceleration.
Prerequisites
PHY-U4-SHM-T1-S1-C1
Common mistakes
Using the pendulum formula at large amplitude.
Combining spring constants like resistances in the wrong configuration.
Keywords
Spring-Mass
Pendulum
Systems
Practice preview
The time period of a simple pendulum depends on which of the following factors?…
easy
A mass 'm' is attached to two springs of spring constants k1 and k2 connected in series. What is the time period of oscillation of this system?…
medium
If the length of a simple pendulum is increased by 44%, what is the percentage increase in its time period?…
medium