An oscillating particle has displacementymetres, whereyis given byy=asin(kt + A)°, whereameasured in metres,tis measured in seconds andkandAare constants. The time for a complete oscillation isTseconds.

Findkin terms ofT.

soTmust be 4x(length of time taken for the particle to move from y=0 to y=a its maximum displacement)

This length of time therefore can be found using sin(kt + A)°=1

sot=(90 -A)/kT=4

sot=(360-4A)/k

now to eliminateAy=0 at t=0, meaning 0=

asin(0 +A)

so sinA =0, A=0

T=360/kIs this reasoning correct?