calculus - Is this enough info to solve this time dilation problem

There are two clocks. One is a regular clock measuring regular time $\tau$. The other is a clock measuring time $t$ which also advances clockwise, but does not advance uniformly--it accelerates w.r.t. $\tau$ from 12 to 6 o'clock, and decelerates from 6 to 12, such that the two clocks always tell the same time at 12 and 6. It is given that the alternating acceleration and deceleration of $t$ w.r.t. $\tau$ is uniform--$\frac{d^2t}{d\tau^2}=K$ where $K$ is a constant. Is this enough info to determine the "dilation" $\frac{dt}{d\tau}$? If not, what other info is needed?