For simple harmonic motion, the displacement x as a function of time t can be expressed as:

x(t)=Acos(ωt+ϕ)

where $A$ is the amplitude, $ω$ is the angular frequency, and ϕ is the phase constant.

Given:

Time Period($12$ seconds

Angular frequency(ω)=2π/T=2π/12=π/6 rad/s

We need the time t when the displacement x(t)=A/2

A/2=Acos(t*π/6 + ϕ)

cos(t*π/6 + ϕ)=1/2

The angle whose cosine is 1/2 is π/3 (or −π/3):

t*π/6+ϕ=±π/3

Assuming ϕ=0 for simplicity: t*π/6=±π/3

t=±2 seconds

The positive solution is:

t=2 seconds

For simple harmonic motion, the displacement x as a function of time t can be expressed as:

x(t)=Acos(ωt+ϕ)

where $A$ is the amplitude, $ω$ is the angular frequency, and ϕ is the phase constant.

Given:

Time Period($12$ seconds

Angular frequency(ω)=2π/T=2π/12=π/6 rad/s

We need the time t when the displacement x(t)=A/2

A/2=Acos(t*π/6 + ϕ)

cos(t*π/6 + ϕ)=1/2

The angle whose cosine is 1/2 is π/3 (or −π/3):

t*π/6+ϕ=±π/3

Assuming ϕ=0 for simplicity: t*π/6=±π/3

t=±2 seconds

The positive solution is:

t=2 seconds